Government Art Collection: At Work, Whitechapel Gallery

Political figures choose artworks from a rarely seen national collection

It owns almost twice as many artworks as the Arts Council, and two-thirds of its 13,500-strong hoard is on display at any given time, yet it’s a collection the public never usually gets to see. Since its foundation in 1898, the Government Art Collection has been purchasing work by British artists not for the nation, but to hang exclusively in the corridors of power, from Downing Street to the British consulate’s office in Azerbaijan. Perhaps, in these cost-cutting times, it now feels impelled to justify its existence to the taxpayer by giving it a taster of its work – though, in all probability, the British taxpayer was probably unaware of its existence till now.

Jean-Marc Bustamante, Timothy Taylor Gallery

Is cheeriness enough to make art?

Who or what is Jean-Marc Bustamante? This, surely, is the question we are supposed to ask of this artist of the affectless, who has skated in his three-decade-long career across the genres – first photography, then Minimalist sculpture, then a merger of the two, and for the last few years these shockingly vivid “paintings” (I use the scare quotes intentionally) on Plexiglass.

Art Gallery: The Museum of Everything

Walter Potter's curious world brought to life in a Peter Blake exhibition of outsider art

Whether you think the weird world of Walter Potter is cute or creepy, there’s little doubt that the Victorian taxidermist, and creator of humorous tableaux in which fluffy creatures enact human scenarios, has acquired some standing in the art world. When his museum collection went under the hammer at Bonham’s in 2003, Damien Hirst, David Bailey, Harry Hill and Peter Blake each bid for valuable items. Now each has contributed to an exhibition that not only recreates part of Potter’s original museum, but invites us to celebrate the quirky art of the outsider artist.

Serge Gainsbourg vs The Anglo-Saxons

How a louche French national treasure became an international cult

The arrival of Gainsbourg: Vie Héroique in British cinemas this week – under its Anglo-Saxon title Gainsbourg – assumes that distributors think there’s an audience. Even so, Gainsbourg hardly has the appeal of a Johnny Cash biopic. Or even an Ike Turner biopic. The release continues a process that began in the early 1990s, when a slow, posthumous rise to recognition of Serge Gainsbourg began outside the Francophone world, au delà de l’Hexagon.

The xx, Somerset House

XX-rated: gloom merchants fail to shine at Somerset House

I don't know exactly what they do in the music classes at Putney’s Elliott School, but it seems to do the trick. Fleetwood Mac's Peter Green went there 50 years ago and now, after admittedly a bit of a lull, the school is positively spitting stars out by the vanload. Kieran Hebden, aka Four Tet, attended, Hot Chip's members are Elliott alumni and The xx are the latest schoolkids on the block, with their self-titled 2009 debut album tipped to be a serious Mercury Prize contender.

Onstage last night, however, the Twilight-style black-garbed trio of vocalist/ bassist Oliver Sim, percussionist Jamie Smith and vocalist/ guitarist Romy Madley Croft revealed the band's limitations as well as their strengths as they studiously worked their way through most of their only long player. There is a fragile beauty to the songs when played at home, but in the flesh most of their material starts to sound a little bit, well, samey. At its best it is timeless minimalist pop, pared down to its bare bones, Chris Isaak meets Philip Glass, as on "Crystalised". But elsewhere there is too much of The Cure and New Order at their gothiest gloomiest. And the simplicity is not always sophisticated. "Heart Skipped a Beat", with its childlike hook, keeps threatening to turn into "Three Blind Mice".

It is never a good sign when one is making notes at a gig and one finds oneself writing, "Must call dentist tomorrow about daughter's teeth." Despite, or maybe because of, the glorious white-walled architectural setting of Somerset House, there were just too many distractions unless you really, as Howard Devoto said in a different context, wormed your way into the heart of the crowd. On the fringes there were those triple threats of the modern live concert, people taking photos of each other, people so excited by the gig they had to ignore it and text their friends to tell them how excited they were, and people nipping off to the bar. Though regarding the latter sin, in mitigation the bar was undeniably appealing, due to the venue organising a speedy and fair queuing system very similar to the one in my local post office. Not that they serve Carling on tap at my local post office.

The still relatively rare sight of a woman on lead guitar is more refreshing than any cold lager, but Madley Croft does little to add to the recorded versions of their songs. Sim is a lithe, lively bassist, bobbing and weaving around the stage as if ducking imaginary missiles, but his banter is largely limited to talking about the "funky house" before the band's positively glacial cover of R&B chanteuse Kyla's "Do You Mind". Only a few tracks really stood the test of live performance. "VCR" – a song title The Human League would surely use if they were starting out today – had a beefed up feel compared to the frankly plinky plonk version on their album and "Islands" retained its itchy, infectious vibe thanks to a nagging riff and Madley Croft’s whispered vocals cross-cutting with Sim’s drawl.

Frustratingly though, the threesome never quite built up more than a functional head of steam. At Glastonbury recently they were joined onstage by Florence Welch minus her Machine for a radical unpicking of "You’ve Got The Love". It would have been a wonderful way to finish with a flourish last night. Instead we got sparkly glitter shot out over the audience and a recorded version of "You’ve Got The Love" as everyone headed for the bus. If any Elliott School music teachers were present I hope they gave their ex-pupils good marks for effort but less plaudits for charisma.

Overleaf: watch The xx perform with Florence Welch

Modern Masters: Warhol, BBC One

Did Andy Warhol change the world? An art critic dons an Andy-suit to find out

I wondered how long it would be before Andy Warhol’s "15 minute" quote came up. From the whizzy, flash-bang opening credits  I knew it wouldn’t be long. I was right: but less than seven minutes? Less than five?  I didn’t time it, since I was still somewhat mesmerised by the sight of perky presenter Alastair Sooke doing a kind of disco-dancey, pointy-arm manoeuvre in front of  Picasso’s Les Demoiselles d’Avignon during the intro. (Oh no,  Alastair, I wanted to cry, you can’t out-cool Andy, so don’t even try.)

Richard Hamilton: Modern Moral Matters, Serpentine Gallery

The medium is the message in Hamilton's body of political works

Richard Hamilton, the true father of Pop art and spiritual descendant of Duchamp, is not a particularly prolific artist. Rather, he sticks to an idea and works on it over several editions and in different media, so that we get a large body of work repeating the same image in paint, in collage, in photography and in mixed media. For Hamilton, now 87, in so much of what he has done over the decades the key idea cannot be conveyed by a single unique work of art, because the key idea is often to do with the multiplicity of images: in other words, the medium is the message.