“I don’t want to be a Cyclops,” Pierre Boulez said in 2010, faced with the prospect of conducting a Chicago concert with only one working eye. Eye troubles, alas, have continued to bedevil the octogenarian giant of contemporary music, which is why his current engagements with the London Symphony Orchestra – there’s also a tour to Paris and Brussels this week, and a second Barbican engagement next Tuesday - have fallen into the hands of a younger composer-conductor of advanced habits, the admirable Hungarian Peter Eötvös.

Donatella Flick, one of Britain's most important arts patrons, is furious. "Madness!" she cries in her lush Italian voice. "This is a country that was fantastic, and now there's a demolition going on, bit by bit!" We're sitting in Sir Winston Churchill's old drawing room - now her drawing room - near Kensington Gardens, and I would give a lot to see David Cameron flinching on her huge black sofa as he got a withering dressing-down.

Critical, urgent, hard - those are the three words used about the challenge to get the rich to pay more for the arts by the new man at the tiller. He should know. Jonathan Moulds, European President at Bank of America Merrill Lynch, is one of the super-successful, super-wealthy financiers to whom the Cameron government is desperately looking to pick up the slack as they cut back public spending. What the government hopes for is modern-day Medicis - arts patrons who use their wealth to back orchestras, performers, theatres and educational projects - and lots of them.

It’s over 30 years since André Previn left his post as principal conductor of the London Symphony Orchestra. But once you’re part of the LSO’s treasured ‘family of artists’, the orchestra never lets go, year upon year inviting you back for Christmas, New Year, weddings, bar mitzvahs, any occasion going. The same with the violinist Anne-Sophie Mutter – briefly in the last decade Previn’s fifth wife, though they share the same platform with just as much ease now that they’re divorced.

Last Tuesday night saw the London Symphony Orchestra celebrating 20^th century English music under the baton of Antonio Pappano, launching proceedings with a stylish (and more than a little sexy) rendition of the dance suite from Thomas Adès’ Powder Her Face. Last night the LSO were back with Adès himself for an evening offering a rather more expansive tour through the composer’s work, pairing its dense orchestral textures with a selection of songs from Mahler’s Des Knaben Wunderhorn.

Just a few weeks ago, John Eliot Gardiner and his Orchestre Révolutionnaire et Romantique delivered what was unquestionably one of the year’s finest concerts – performing Beethoven’s Fourth and Seventh Symphonies with more wit, swagger and verve than even the mighty Leipzig Gewandhaus could muster. Returning to Beethoven last night with the very different orchestral forces of the London Symphony Orchestra, the question was surely whether Gardiner could summon the same magic for a second time.

Praise be, or slava if you prefer, to Valery Gergiev for honouring new Russian music alongside his hallmark interpretations - ever evolving or dangerously volatile according to taste – of Prokofiev, Shostakovich and Stravinsky. Last LSO season featured some of the less than inspired recent works Rodion Shchedrin has been dredging by the yard. Yet few would begrudge the palm of deep and original musical thought to this past week’s heroine, Sofia Gubaidulina.

Highly finished literary tales of doomed nixies, like Hans Christian Andersen's The Little Mermaid, seem to have prompted reams of bad art but plenty of mellifluous music. Not even all of that is on the same level. Viennese late-Romantic Zemlinsky's loose-limbed three-part Andersen homage has long floated in a limbo somewhere below the more curvaceous forms of Dvořák's Rusalka and Sibelius's The Oceanides, and not just because of unfavourable historical circumstances (the composer withdrew the work after its 1905 premiere, and it did not resurface until 1984).

On Thursday the London Symphony Orchestra plays a night of epic movie music by the man who gave America’s cowboy heroes their most stirring tunes. Dimitri Tiomkin was one of Hollywood’s film-score giants, John Wayne’s choice as composer for The Alamo, Wayne’s magnum opus, and Tiomkin's was the music that urged Gary Cooper and Clint Eastwood to ride out in iconic glory in landmark adventures such as High Noon or Rawhide.