“Previously on Wolf Hall…” It’s been nine years since Claire Foy memorably trembled her way to the block as Anne Boleyn, recapped at the start of the second and final season of the BBC’s handsome Hilary Mantel adaptation. It’s a deathbound affair for all, though.

As an actor, Mark Rylance specialises in outsiders and eccentrics, outliers of one kind or another. He identified and developed his latest character himself, based on the real-life, mid-19^th century Hungarian doctor whose pioneering, lifesaving discoveries were long ignored by the medical Establishment – who in his lifetime was a tragic pariah rather than the hero he should have been. 

“A man walks in,” Leonard (Mark Rylance) begins. “What about him can you observe? What does a man like to be? And who is he underneath?” Leonard is, in common parlance, a Savile Row tailor – “a cutter from the Row,” he insists – fetched up for murky reasons in 1958 Chicago, where his shop’s best customers are sharp-dressed Mob clan the Boyles.

“No one can say you didn’t try,” shipyard worker Maurice Flitcroft (Mark Rylance) is told, shortly before bluffing his way aged 46 into the 1976 British Open, having never played golf before.

Claire van Kampen has a history of providing roles for her husband, Mark Rylance. He starred in her critically acclaimed Farinelli and the King three years ago, and now she directs him as Iago in the Globe's production of Othello, with Moonlight actor André Holland as the eponymous general.

Mark Rylance was once renowned for skipping thank yous to agents, friends and everyone he’s ever met in award speeches and instead giving us a blast of Minnesotan prose poet Louis Jenkins. Now the two men have co-created an oddball meditation, first seen in New York earlier this year, in which comedy meets soul-searching on an untethered frozen lake.

Two cultural giants from different spheres align to occasionally sublime results in The BFG. Steven Spielberg's film locates the beatific in its (literally) outsized star, Mark Rylance, but lapses into the banal when its eponymous Big Friendly Giant – Roald Dahl's 1982 literary creation made motion-capture fresh – isn't careering across the screen.

As a sort of companion piece to E.T., which shares this film's screenwriter, Melissa Mathison, who died last year, the film brings an otherworldly presence into our world of the everyday. And yet there remains something pro forma about the abiding feel of a movie that doesn't break much thematic or emotional ground. It allows its Oscar-winning leading man to continue his conquest of celluloid following a life spent mostly on stage. But Rylance aside, the rest of a game English cast can politely be said to be along for the ride, though I doubt Dame Penelope Wilton – as she now is – ever thought she'd get to play the Queen and fart at the same time: how jolly!

The Elizabeth II sequences arrive relatively late in the day and are the least engaging aspects of a venture that is so beautifully anchored by Rylance with his kindly yet baleful eyes that one slightly cringes as and when The BFG turns into an ad hoc advertorial for the royals: Visit Britain will have something new on which to hang its hat. Meanwhile Rebecca Hall and Rafe Spall the rest of a name English – both playing personnel of the Palace – add a Spielberg title to their CVs. If only either actor were in any way challenged by what they are asked to do; Wilton (pictured above), for her part, sticks to a general air of bemusement throughout. 

Far better is anything involving the dream-friendly creature of the title, a being as large-eared as he is thin-necked to whom Rylance imparts a wounded beneficence. Applauded all the way to an Academy Award for his debut assignment for Spielberg on Bridge of Spies, the determined maverick that is Rylance clearly meets this uber-mainstream director more than halfway, and one is heartened to hear that the pair have two further collaborations on tap. (Move over, Martin Scorsese and Leonardo DiCaprio.)

Noted for language that might give even Edward Lear or James Joyce pause, the BFG intersperses his cod-philosophising about dreams with words like Frobscottle (the fizzy beverage shown above), "glummy", and (my favourite phrase) "a dibble of despair" – utilised by the BFG as a way of envisaging a mostly but not entirely rosy future for Sophie (Ruby Barnhill), the bespectacled 10-year-old who finds in the giant at once an ally, chum, and escape route from her Dickensian routine. Not for nothing is the charming, commendably unaffected Barnhill glimpsed reading Nicholas Nickleby. 

The BFG is brought down to size by the bullying like of the Fleshlumpeater (Jemaine Clement), one of a forbiddingly beefy brigade of nasties who are less generously inclined to Sophie than her new-found protector-friend. Kids will doubtless surrender to the occasional grossout value of the Giant Country goings-on, but Spielberg seems far more naturally suited to the earlier meanderings of his camera around and above a storybook London of ghostly, largely Georgian charm. Let's just say that the scene-setting is more alluring than what happens once we actually settle in.

And Rylance is a softly spoken, gently accented wonder throughout, his character's innocence a comfort to the parentless Sophie and a rebuke to almost everyone else. So what if in his socially maladroit state the BFG sends one of the Queen's Louis XIV chandeliers crashing to the ground? Possessions, the film at its best reminds us, can be replaced (well, maybe not in that case). In his state of grace, Rylance's BFG allows a comparatively prosaic Spielberg offering access to the ineffable realm of the poetic.

• Read more film reviews on theartsdesk

MARK RYLANCE’S BIGGEST HITS ON STAGE AND SCREEN

Bridge of Spies. Spielberg's warm-hearted Cold War thriller is lit up by Tom Hanks and Mark Rylance

Endgame. In Complicite's homage to Beckett, Rylance's Hamm is an animated, self-lacerating lout

Farinelli and the King. A witty and moving new play is a timely reminder of just why art matters

Jerusalem. Rylance is unforgettable as Johnny Rooster Byron in Jez Butterworth’s smash Royal Court hit

La Bête. Rylance dazzles in astonishing opening monologue, but this callow play coasts on the performances

Nice Fish. Rylance is waiting for cod-ot in this absurdist West End trifle

Twelfth Night/Richard III. Rylance doubles up as Olivia and the hunchbacked king (pictured above) for Shakespeare's Globe

Wolf Hall. Mark Rylance works rare marvels as Hilary Mantel's scheming Tudor fixer

PLUS ONE TURKEY

Much Ado About Nothing. Rylance Old Vic staging of Shakespeare's romantic comedy with elderly leads gets lost in translation

Overleaf: watch the trailer for The BFG

Nostalgia for the good old days of mutually assured destruction? You’d have got long odds on such a thing on 9 November 1989, the day the Berlin Wall was breached. A quarter of a century on, the Americans and the Russians are entangled in a whole other theatre of war in which the idea of negotiating with the enemy is unthinkable. The Soviets may have been abominable commie bastards but, hey, our guys could still clink a glass with them. So Steven Spielberg is able to visit the Cold War in something like a spirit of levity.

Bridge of Spies is much more overtly an entertainment than Schindler’s List and Saving Private Ryan. It’s also an unapologetic defence of American exceptionalism, as embodied in Tom Hanks, an actor who has inherited Jimmy Stewart’s ability to project intelligence matched by integrity. He plays James B. Donovan, a wily insurance lawyer who once upon a time was a prosecutor at Nuremberg. When a Soviet spy called Rudolf Abel (Mark Rylance) is hunted down in Brooklyn, he must be given an American version of a show trial: one in which the wheels of justice are seen to turn, and the accused is given a proper defence. Step forward, Donovan, reluctantly anticipating opprobrium and trouble for his suburban nuclear family of three kids and delectable wife (Amy Ryan, pictured below).

The complication is the CIA and the legislature don’t want Abel to get off the hook. Donovan's instinct, over which he has no control, is to give them a working lesson in the meaning of the constitution (see clip overleaf). Even Abel warns Donovan to go carefully. His advocacy works up to a point. Abel is spared execution, Donovan pleading that he may be useful as a bargaining chip when America wants to retrieve one of her own. Sure enough, a pilot on a top-secret high-altitude mission over Soviet space is promptly shot down in his U2 spy plane and fails to inject himself with poison to avoid falling into enemy hands. Donovan is sent to Berlin as a private individual to negotiate an exchange. Donovan being Donovan, and Spielberg enjoying a tilt against the odds, he tries to get two for one: the pilot, plus an American student caught on the wrong side the day the wall was erected.

This spin down memory lane, a great deal of it more or less based on fact, is the brainchild of Matt Charman, promoted to nosebleed territory from writing scripts for British television about family zoos and police skulduggery. He shares his credit with Joel and Ethan Coen and between them they have cooked up an intensely gripping thriller. The Coens, you suspect, were responsible for tugging the geopolitical face-off towards gentle caricature. The senior KGB encountered on the front line in East Berlin are saturnine but robustly comic, while much fun is had twitting the frustrated pawns representing the DDR. The boot is on the other foot for Sebastian Koch, more spied upon than spying in The Lives of Others but here playing East German lawyer Wolfgang Vogel.

As for the look of the film, America is all polished wood and purring motors, while the spirit of Deighton and Le Carré is invoked in the grim greyness of Berlin on both sides (until we penetrate the Soviets’ plush embassy, that is). Spielberg does what only he can with a camera. He zooms shamelessly in to flag up psychological dilemma. For the moment the spy plane crashes, the clatter of plunging metal evokes that coach dangling over a cliff in Jurassic Park. The denouement is second only to ET for outright emotionalism. If the film has a flaw, it’s that the stories of the two captured Americans go for next to nothing, especially that of Francis Gary Powers, the pilot who was widely condemned for allowing himself to be captured.

The film’s headlining novelty is Mark Rylance, who plays Abel with a vaguely Scottish accent as a poker-faced innocent with quite as much time to think and stare as Thomas Cromwell. He even gets a catchphrase. “Would it help?” he asks when Donovan wonders why he doesn’t look worried (see clip overleaf). Like the early scene in which he extracts a secret message from a tiny contraption (pictured above), the performance is mesmerising in its pernickety attention to detail. His scenes with Hanks are the riveting heart of this compelling - if not always plausible - comic-book history lesson.

Bridge of Spies really is the spy game as just that: a game whose horrors Spielberg has thrillingly sanitised.

MARK RYLANCE’S BIGGEST HITS ON STAGE AND SCREEN

Bridge of Spies. Spielberg's warm-hearted Cold War thriller is lit up by Tom Hanks and Mark Rylance

Endgame. In Complicite's homage to Beckett, Rylance's Hamm is an animated, self-lacerating lout

Farinelli and the King. A witty and moving new play is a timely reminder of just why art matters

Jerusalem. Rylance is unforgettable as Johnny Rooster Byron in Jez Butterworth’s smash Royal Court hit

The BFG. Rylance lends moments of the sublime to standard issue Spielberg

La Bête. Rylance dazzles in astonishing opening monologue, but this callow play coasts on the performances

Nice Fish. Rylance is waiting for cod-ot in this absurdist West End trifle

Twelfth Night/Richard III. Rylance doubles up as Olivia and the hunchbacked king for Shakespeare's Globe

Wolf Hall. Rylance works rare marvels as Hilary Mantel's scheming Tudor fixer

PLUS ONE TURKEY

Much Ado About Nothing. Rylance's Old Vic staging of Shakespeare's romantic comedy with elderly leads gets lost in translation

TO THE RESCUE: TOM HANKS SAVES THE WORLD (AND SOME IFFY MOVIES)

A Hologram for the King. Tom Hanks is the reason to see Dave Eggers's sentimental Saudi comedy

Captain Phillips. Piracy drama prompts bravura all-action display from director Paul Greengrass and captain Hanks

Cloud Atlas. Star company assumes various guises as David Mitchell's time-travelling masterpiece is lovingly told in under three hours

Extremely Loud and Incredibly Close. Oscar-nominated adaptation of Jonathan Safran Foer's novel is lacking in magic

Saving Mr Banks. Emma Thompson as PL Travers and Tom Hanks as Walt Disney track the journey of Mary Poppins from page to screen

Sully: Miracle On The Hudson. Eastwood and Hanks are the right men for an epic of understated heroism

Toy Story 3. To infinity and no further: Woody and the gang (sob) go on their final mission

PLUS ONE TURKEY

Inferno. In Dan Brown's dumbed-down Florence, Tom Hanks saves the world. But not the movie

Overleaf: watch clips from Bridge of Spies

No doubt this sophisticated bagatelle starring Mark Rylance worked like a charm in the intimate space and woody resonance of the Sam Wanamaker Playhouse.

Wolf Hall divided viewers from the off. It mesmerised many and left a vocal minority cold, for whom apparently - mystifyingly - it has all been a bit dull. The dialogue was too elliptical, the politics tricksy and convoluted (who is this Holy Roman Emperor anyway?), there was a surfeit of men called Thomas and women stitching in bay windows and big dresses.