This Wednesday night, 23 July, one of the great pioneering bands of electronic music will be doing something bold: leading their own classical Prom. "For one night only, I'm one of the BBC singers!" marvels Pet Shop Boys frontman Neil Tennant – he is adding his voice to the 18-strong chamber choir.

"I can't imagine he'll blend in," deadpans his colleague Chris Lowe, who is usually found hiding behind a bank of synthesisers at their shows. He is worried about the lack of dry ice and lasers at the Royal Albert Hall. "The lights are always on [at classical concerts], aren't they? I personally am going to feel very exposed."

It is not the first time a pop group has featured at the Proms. From Soft Machine's 1970 set (later turned into a live album)to last year's 6 Music and 1Xtra specials, pop and rock acts have often played a part in the two-month series. But Tennant and Lowe are doing something different this year: performing the world premiere of an ambitious new work, A Man From The Future. Based on the life of the extraordinary mathematician and Enigma code-cracker Alan Turing, it's an orchestral pop "biography" in eight parts for electronics, orchestra, choir and narrator.

It takes in Turing's Dorset childhood, the paper that laid down his theories for the modern computer, his second world war success at Bletchley Park, his conviction for gross indecency in 1952 (after innocently telling a police officer about his homosexuality), his opting for chemical castration over imprisonment, his depression and eventual suicide.

This project is not out of character, given the Pet Shop Boys' recent career: they have also written a film soundtrack, ballet score, musical and children's play in the last 15 years.

Tennant explains that they first heard of Alan Turing in the mid-80s after seeing Hugh Whitemore's West End play Breaking the Code: "You really get a feeling of this extraordinary quirky genius when you learn about Turing. [He] made a big impression on people that knew him, because he was such an unusual person … coming from this different era of V-neck sweaters and sports jackets, yet having this incredible vision of the Universal Machine, and going round telling people he was homosexual."

In the 80s, though, Turing's story resonated differently. "Back then, I knew nobody who owned a computer. Fifteen to 20 years later, everyone had one. Also [in the 80s] homosexuality between men was only legal in private over the age of 21 – and of course that situation has changed. Essentially, we've all caught up with Alan Turing."

The band's interest in Turing returned after Lowe watched a 2011 Channel 4 documentary on the polymath, prompting Tennant to read Andrew Hodges's biography, Alan Turing: The Enigma and the pair to start composing A Man for the Future. Falling in love with Hodges' poetic prose, Tennant emailed the author in late 2012, asking him to help choose passages for the libretto that would best tell Turing's story.

Hodges – a lifelong Pet Shop Boys fan and gay rights campaigner – was delighted. "It's very direct," he says of the final work's lyrical style. "Each episode goes to the very centre of what's going on … it's not just alluding to it or inspired by it."

After finishing the piece together, however, events changed its shape. Last Christmas Eve, Turing was awarded a posthumous royal pardon overturning his 1952 conviction for gross indecency. "Dr Alan Turing was an exceptional man with a brilliant mind," said the justice minister, Chris Grayling, who made the formal request for the pardon.

This prompted mixed feelings for Hodges. "I don't think it's right in principle to make an exception for one person on the grounds of what they did for the state," he explains. "It should be for everyone who was in that situation." Nevertheless Tennant and Lowe explicitly address this contradiction in their piece's finale, which pleases him. "The fact that a public work like this [is] going ahead in the very centre of one of our most famous concert series, on the BBC … there's a sense of making up and making good, of expunging a lot of what was so bad about the old world."

"We had to [rewrite the ending to] point out that the convictions of tens of thousands of other men remain, and that hasn't really been discussed," says Tennant. However, the finale has a celebratory feel, and recognises the changes in attitudes towards homosexuality, globally. Tennant lists these happily: a 2013 US poll in which 52% of Americans were shown to approve of same-sex marriage, the moment in 1994 when John Major lowered the age of consent to 18 ("everyone forgets it was him that started things off").

On a personal level, there was also the reaction to a text he sent to one of David Cameron's special advisers, after the Pet Shop Boys were asked to play at the 2012 Olympic team's winners parade. "It was a bit cheeky," he laughs now, of the text he sent after the concert, "but it suddenly occurred to me … as David Cameron is so with the gay agenda, I wondered if [the rumour of the royal pardon] was really true." Tennant's text was direct: "Could you pass on to the prime minister that in Alan Turing's centenary year it would be an amazing inspirational thing to do to pardon him?"

"I didn't think it was going to happen," Tennant adds, especially as Gordon Brown had in 2009 issued a government apology but rejected calls for a pardon. "But what was interesting was the bloke I sent it to responded immediately. And so I thought, 'oh, they obviously do know about this'."

Having played anti-section 28 concerts at the beginning of the Pet Shop Boys' career, did he find it odd that a Conservative prime minister supported gay rights so strongly? Tennant responds diplomatically. "It isn't really a party political issue any more. I think what really happened is we've moved, not totally, but as a society, away from toleration to acceptance, and a reasonably happy acceptance actually. All parties are supporting that now." Did he question Cameron's motives? He pauses. "You'd have to ask David Cameron about his motives, because I know what certain people say about it. Nonetheless he's run with this issue."

The work was picked for the Proms after Tennant had a chance meeting with outgoing Radio 3 controller Roger Wright last year ("and he immediately said, 'We must have this as a Late Night Prom,' so that was fantastic"). Tennant is the band's classical music buff; he is currently enjoying an obsession with Stravinsky's spoken-word piece The Soldier's Tale. Lowe – the classically trained musician of the pair – has also enjoyed making connections with Turing's original work. Writing music for the BBC orchestra on his laptop, and marrying traditional music with computer-generated sounds, he loves how the Pet Shop Boys are telling Turing's life story through the machines he, in effect, invented.

The prom will also feature the band's 1991 overture to their Performance tour, and continues their tradition of working with women. On Wednesday, Chrissie Hynde will sing orchestral versions of Pet Shop Boys songs in the concert's first half, while Juliet Stevenson will narrate Turing's story in the second. But one man will be the prom's focus, and Tennant makes no apology about that. "We wrote it for Alan Turing."

A Man From The Future will be performed on 23 July