Three decades and 11 albums in, Neil Tennant and Chris Lowe still feel like they are renting their place as unlikely pop stars

On the stage of HAU 1, a theatre in the Berlin hipster district of Kreuzberg, the Pet Shop Boys are performing a dress rehearsal. To the left, Neil Tennant stands at the microphone, smartly dressed and straight-backed. To the right, Chris Lowe pecks impassively at his keyboard, his eyes obscured by a curious hat: French Foreign legionnaire meets North Sea trawlerman.

Their hair may be greyer and sparser now, the clothes more expensive, but the scene is much the same as their first TV appearances back in 1985. Though outlandish costumes and colourful stage sets come and go – during the Olympics closing ceremony they circled the stadium on an origami rickshaw, wearing pointy hats — their image remains fundamentally unchanged. "The guy on keyboards who doesn't smile and the singer who looks a bit uncomfortable," says Tennant. "That's the act." Tennant and Lowe. Neil and Chris. Pet Shop Boys.

The working title of their 11th album, Elysium, was HappySad; in their very first music-press interview, Tennant paraphrases, "we said our music was happysad because it made you feel like dancing and crying at the same time. The template's never altered that much." Elysium, which was inspired by a walk through Elysian Park in Los Angeles, "fitted in with the weird theme of death with optimism that runs through the album."

Lush and low-key in the vein of Behaviour (1990) and Release (2002), Elysium is a left-turn after the full-blown pop of recent years: their all-the-frills Pandemonium tour took in a triumphant Saturday night at Glastonbury and eight stadium shows supporting Take That. (The boy band's tick-shaped career path fascinates Tennant. "It's an incredible story," he marvels. "It's like Henry IV Part II or something.")

Lowe wanted Elysium to have one unbroken mood. "I always do," he says, eating lasagne in the duo's dressing room. "Either up or down. I don't want to spoil it with a jarring bit of dance-pop in the middle."

"We put some jarring dance-pop in the middle," says Tennant. "Which I notice is the one [A Face Like That] everyone likes."

"Of course they bloody do," says Lowe.

Listen to Elysium

A Pet Shop Boys interview is a show in itself. Tennant is erudite and inquisitive, illustrating points with quotes from Noël Coward and New Yorker cartoons. Lowe stays silent unless he's either laughing or making Tennant laugh, which seems to me a faultless interview strategy. Thirty-one years after meeting in a Kings Road hi-fi shop, their friendship seems invincible.

It was not the plan but the duo soon realised Elysium contained several songs about the passing of time. "We're not embarrassed to confront age," says Tennant, who is 58. "There's the paradox of making pop music when you're in your 50s. People weren't meant to be doing that originally and yet they are. Mick Jagger [used to say] we're not going to be doing Satisfaction when I'm in a wheelchair."

"Although it would be quite an appropriate song to sing," says Lowe. A diehard lover of disco and rave, he seems less comfortable being reminded of time's arrow. "People are always saying to us, oh, it's 10 years since you did this or that," he grumbles. "It's neverending. You're always 10 years from something." One new song, Your Early Stuff, is drawn from conversations with taxi drivers. "Oh you're him from the Pet Shop Boys aren't you?" Tennant mimics. "I suppose you're more or less retired now. It's quite a journalistic thing as well. The early stuff is always the holy grail: the pure years before money and fame."

The Pet Shop Boys' success – 39 Top 20 singles, 100m records sold – feels natural in retrospect but it was completely counterintuitive when they started. They demonstrated that you could come to pop late, make hits from improbable material (debut single West End Girls was inspired by Grandmaster Flash and TS Eliot) and present them without smiling – even, on the cover of 1987's Actually album, while yawning. Their anomalous presence at the chart's top table shaped many fans' understanding of what pop could be: witty, stylish, literate, unpredictable, sincere but not overly invested in asserting its sincerity. Not that it was easy.

"There's a myth about us that the hits were coming and it was all great," says Tennant. "Actually it was a bitter 24-hour struggle. Always arguments. A friend of ours asked someone at EMI: "How long do you think this is going to last?" And he said: "Four or five singles." And I thought, you know what? He's probably right." He laughs. "Although I'm joking, in a way I do feel like that. I don't feel secure. I never believe there's a moment when you climb on to the plateau and you're there. I still feel like you're just renting the space."

The pop world has dramatically changed around them. One thing Tennant liked about the closing ceremony was its echoes of the old days of Top of the Pops, when you'd rub shoulders with friends and enemies alike: "Sitting in the green room with One Direction talking to the Spice Girls and Annie Lennox holding court in the corner. You don't really meet people these days." Much of the business of selling a record in the 21st century makes them grimace. They cherish record shops and despair at online piracy. "There's a famous argument: music should be free like water," Tennant says. "To which I say, have you seen London water rates recently?" They stopped posing for fan photographs because they didn't like ending up on Facebook pages, though they're still happy to sign "an old-fashioned analogue autograph".They gave up Twitter after two years; Lowe thinks social media is "so egotistical, it's just horrendous really". Tennant agrees. "There's a false intimacy, which is I think why people get so angry. People tweet a celebrity and they get no response. It's a totally fake relationship."

Contrary to the kneejerk assumption that rock is raw and authentic and pop cynical and ephemeral, the Pet Shop Boys have maintained their core principles longer than most. There are still things they won't do, like red carpet appearances or anything to do with the Royal Family. "What we have done since the beginning is try to keep the purity of the project," says Tennant. "We haven't, as they used to say in the 70s, sold out." That said, he sighs, "doing everything the difficult way is wearying sometimes".

Another index of their integrity is their attitude to extracurricular projects. Over the past decade or so they have composed a West End musical, a ballet, a new score for Battleship Potemkin and songs for Robbie Williams and Girls Aloud, but always as a duo. You never see Tennant being Mr Clever on Question Time or QI.

"When you're an articulate pop star you get asked to do a lot of things like that," he says. "I've never wanted to be a talking head. I can't be bothered. I was asked if I wanted to be considered to be a judge on American Idol. I was quite excited and then …" "You saw the programme!" laughs Lowe.

The Pet Shop Boys have a funny relationship with fame. Although they sometimes move in glittering circles – an anecdote about the last time they saw the late Robin Gibb involves Karl Lagerfeld, Mikhail Gorbachev and Lech Walesa – they tend to regard celebrity from the vantage point of privileged observers rather than paid-up participants. They have maintained their privacy well. Their love lives are virtually a mystery, although Tennant's lyrics indicate a romantic soul, forever cycling between caution-be-damned elation (Love Comes Quickly) and back-to-earth disappointment (So Hard). "I find it interesting," he says. "The gap between the ideal and the reality is one's life anyway."

At least the partnership that has defined his adult life endures. The duo have enough songs to complete another, more electronic album soon and are working with the BBC Philharmonic on a piece of music about Alan Turing, the codebreaker and computer pioneer who was prosecuted for homosexuality ("A terrible story," says Tennant. "Of course the reason they won't pardon Alan Turing is because they'd have to pardon all those homosexual men. Well why don't they? Why don't they pardon them all, actually?"). A few days after we meet, they play to the Team GB parade outside Buckingham Palace, doubtless surprising many taxi drivers.

After the live-streamed Berlin show, which features most of Elysium and a lovely cover of Robin Gibb's I Started a Joke, there are drinks in the bar. Tennant wanders over looking a bit tipsy: more mischievous and gossipy. One of the German promoters teases him for mentioning Elysium's Japanese midweek chart position during the show but Tennant defends it with a Wildean flourish: "You should always celebrate your successes because someone else will celebrate your failures."

In one corner of the bar there is a vast, ornately iced cake to mark the occasion. There are two fondant figures perched on top: the one on the left looking smart in black, the one on the right in hat and sunglasses. Tennant and Lowe. Neil and Chris. Pet Shop Boys.

The journalist's trip to Berlin was paid for by Parlophone Records.