I am standing in the Pussy Riot church, although I'm not really supposed to call it that. Also known as the Cathedral of Christ the Saviour, this vast and ornate building occupies a prominent position on the Moscow river. It was here, in February, that Pussy Riot staged their now notorious performance-cum-protest against what they see as Putin's intolerance. I have come here after a visit to the Pushkin Museum, where another, less vociferous musical radical has been taking centre stage.

Benjamin Britten's art collection has been shipped over from the Red House, his former home in Aldeburgh, and is being shown alongside letters reflecting his close relationship, in the 1960s and 70s, with composer Dmitri Shostakovich and cellist Mstislav Rostropovich. Bizarrely, at a time when Russia is cracking down on protest and enacting laws against gay "propaganda", Moscow is choosing to celebrate the centenary of a gay pacifist composer, the ultimate social outsider.

The museum's show is part of a Britten festival that has already seen events in Saint Petersburg and will culminate in the Russian premiere of Britten's final opera, Death in Venice, at the Moscow conservatoire. "Who would have thought we'd be doing such a quintessential English composer and a piece with this subject matter in Moscow in 2013?" says Peter Coleman-Wright, the Australian-born baritone and Britten specialist, who tells me proudly he has sung in all his operas.

The subject matter is delicate because, based on Thomas Mann's novella, Death in Venice deals with a middle-aged writer's passion for a teenage boy spotted in a hotel on the Lido and lusted after to the point of madness and death. So this homosexual and perhaps even paedophilic work (though the tortured writer Aschenbach and the boy Tadzio do no more than exchange glances) by a gay composer who was excessively fond of teenage boys, is now being performed in a country that, officially at least, has no truck with homosexuality. Tricky.

"The gay side of the opera can't be denied – he falls in love with a boy," says Richard Jarman, director of the Britten-Pears Foundation, which with the British Council co-financed the festival. "But we hoped that wouldn't create a problem." It was a gamble, though. English National Opera's production of Britten's A Midsummer Night's Dream, set in an English public school in the 1950s and with a paedophilic subtext, caused controversy in Moscow last year, while a new Russian-made film about Tchaikovsky has been at pains to excise his gayness. So an opera with lengthy homoerotic ballets was unlikely to be embraced by the fundamentalists currently engaged in a cultural war with those who want to westernise and liberalise Russia.

Ian Bostridge sings Aschenbach in Death in Venice: 'Russians don’t hold back emotionally and that’s what Britten really liked.' Photograph: British Council

The fact that the opera was being given a concert performance and the lithe, god-like Tadzio is never seen in his swimming trunks – never seen at all, in fact – made it less problematic. Jarman insists he had originally hoped to mount a stage production and that the choice of a concert performance was logistical rather than diplomatic, but he accepts it makes the premiere less provocative. "If it was staged it would probably be more of an issue. Certainly some of the productions I've seen would be quite an issue. There was one production I saw in Barcelona in which, in the nightmare scene, Aschenbach dances naked with the boy. I'm quite glad that's not happening here." Had it done so, we might well have been entering Pussy Riot territory.

In this political maelstrom, the British Council has to swim carefully. Paul de Quincey, head of the organisation in Russia, tells me he took up the job in 2011 when anglo-Russian relations were still frosty. Since then a thaw has set in and, as well as backing the Britten festival, the British Council will next year be co-operating with the Russian culture ministry on a wide-ranging series of events gathered under the umbrella of an anglo-Russian year of culture. We are getting Chekhov and Pushkin; they are getting early Hitchcock and James Bond. Who has the better deal depends on your view of art – Russia's cultural apparatchiks tend to favour timeless masterpieces. British art will also be represented by exhibitions on the influence of Oscar Wilde and the work of Francis Bacon, which may appeal more to the Pussy Rioters than the Putinites.

Happily, Moscow, a sharp-elbowed, traffic-clogged, open-all-hours city, has no difficulty accommodating both. Elton John is in town for a sold-out concert, and takes the opportunity to lambast Russia's "inhumane and isolating" anti-gay legislation during his show. He does not repeat the criticism at the concert he gives the following night in the Volga city of Kazan, 500 miles to the east, though. What is acceptable in dynamic, affluent, westernised Moscow does not necessarily play well in heartland Russia. Death in Venice staged in Novosibirsk would be an interesting proposition. Tadzio would have to dress a little more demurely, and not just because of the extreme cold.

Benjamin Britten, right, rehearses with Mstislav Rostropovich in Moscow in 1963. Photograph: British Council

Britten is being celebrated in Russia because in the last 15 years of his life – he died in 1976 aged 63 – Russian musicians, in particular Shostakovich and Rostropovich, became very important to him. Both were regular attendees at the festival in Aldeburgh run by Britten and his partner Peter Pears; Britten wrote several pieces for Rostropovich; and Shostakovich dedicated his 14th symphony to his English counterpart. As part of the festival, that work is paired with Britten's violin concerto in a concert at the conservatoire, with Mark Elder conducting the Russian National Orchestra.

Mikhail Fikhtengoltz, programme manager at the RNO, says the festival is designed to evangelise on behalf of Britten and British music generally. "Both Britten and the British musical heritage are very underrated here," he says. "We know some Britten – the War Requiem, The Turn of the Screw, some of his chamber works, a few of his songs, but otherwise it's still a space that needs to be filled. Elgar and Vaughan Williams are even less well known, and as for Finzi, Bax, John Ireland, Ivor Gurney, nothing." Fikhtengoltz says British music doesn't easily fit with the Russian mentality. "British music invites you to reflect and analyse. It never hurries you up. We need the sheer expression of emotion and drama, and that is sometimes lacking for us."

I experience Russian emotionalism at first hand, because I'm staying at a flat belonging to the Vakhtangov theatre and on the day I arrive a distinguished member of the company, 85-year-old Yury Yakovlev, dies. His body is placed in an open coffin on the theatre's stage, and fans file past and lay flowers. Ian McKellen may be admired in the UK, but you can't quite imagine this scene playing out at the Theatre Royal, Drury Lane. Actors, especially those who took on the role of interpreters of life during Soviet times, are accorded extraordinary reverence, and theatregoers are the weepiest I've ever encountered. The Vakhtangov's powerful and beautiful Eugene Onegin (not Tchaikovsky's opera but Pushkin's verse drama, which will come to London in January 2015 as part of the anglo-Russian year of culture) reduces many of the audience to tears when I see it a couple of days later.

Ian Bostridge, who is singing Aschenbach in Death in Venice, insists Britten's music can tap into that emotionalism, and is far from being as austere and intellectual as it is sometimes presented. "Russians don't hold back emotionally and that's what Britten really liked," he says. "People sometimes looked at his music and thought, rather bizarrely, that it was modern music, and of course in one sense it is, but it's so not modern in another sense. It's very emotionally connected, and if it's played and sung with passion that's what makes the difference." Bostridge believes the apparent detachment springs from Britten's "hidden sexuality" and the way he used theatrical framing devices to mask the rawness of his feelings. "He lived a life of masks and also felt that slight English embarrassment about feeling," he says, "but his music is intensely passionate."

Death in Venice is being conducted by 82-year-old Gennady Rozhdestvensky, who was part of Britten's close-knit Russian circle and conducted the concert at the Royal Festival Hall in September 1960 at which Britten first met Rostropovich and Shostakovich. The neat circularity of having him on the podium for the premiere of Death in Venice is constantly referred to. I corner Rozhdestvensky in his dressing room in between rehearsals and ask what he recalls of Britten. "He was such a shy person," he says. "He was so shy that sometimes you felt he wanted to go out of the room. You got this strange feeling that somehow you were interrupting him and stopping him creating new work. He would be talking very politely to you and answering all your questions, but you knew he was in a world very far away."

Early in the rehearsals, the three singers who have come to Moscow for the performance – Bostridge, Coleman-Wright and countertenor Iestyn Davies – are a little downcast. The tempi are too slow; the pronunciation of the chorus and of the students singing the smaller parts bizarre; the young members of the conservatoire orchestra struggling to come to terms with Britten's soundworld. But over the five days of rehearsal the performance takes shape, and despite bronchial problems induced by the Russian winter their spirits lift.

Benjamin Britten conducting in Moscow in 1964. Photograph: British Council

"It's not Britten and Pears Aldeburgh perfection," says the genial Coleman-Wright after the final rehearsal, "but it's magical in its own way. The players don't have anything to measure it by. They're coming fresh and open, and doing it for the first time. There's no preconceived idea of how it should go. They're not trying to copy anybody. They're just being true to what they feel. They didn't quite grasp the whole structure at first, but they have really embraced it now and want to make it work. It's a unique soundscape for them. Some of the young small-part singers are coming up and asking us how to do things, and that's fabulous. It's wonderful to do such a masterpiece outside of Britain, where it's always expected to be perfect. This has a whole different flavour."

During the interval of the performance, the three visiting singers worry that the audience are not quite getting it: the long first act can be daunting, especially for first-timers. But the tumultuous reception after the second act eases their fears. When Rozhdestvensky holds up the score, the hall – the very hall at the Moscow conservatoire in which Britten conducted the premiere of his cello symphony with Rostropovich as soloist in March 1964 – erupts. Afterwards, Jarman is happy and perhaps relieved that four years' work has paid off. "Death in Venice," he says, "has been well and truly launched in Russia."