Years & Years: From feeling like the weird kid at school and studying architecture to the Ben Whishaw effect

Olly Alexander had an inkling that Ben Whishaw could dance. Perhaps he had more than an inkling; the lead singer of Years & Years was good friends with the actor (Q in the Bond films), and it's entirely likely he had first-hand experience.

And so when he and his electro-pop bandmates – the bassist Mikey Goldsworthy and the synth player Emre Türkmen – had had enough of being a best-kept secret tucked away on an indie label, they asked Whishaw to appear in a video for their single "Real". The band had no money, and the video would be largely funded by Türkmen himself, but it would be eye-catching nevertheless: Whishaw dancing alone in a club, limbs flailing, while Alexander watches mournfully on.

"He's a very good dancer, isn't he?" Alexander says now.

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He's right, Whishaw can move, and "Real", a gossamer-light dancefloor filler with a keen hook, was well served by its accompanying promo. It became something of a minor viral sensation – eight-and-a-half million views – and got the band the attention they craved. Polydor signed them, and after five years of plugging away, they suddenly shifted up several gears. In January, they were announced winners of the BBC Sound of 2015 poll, following in the footsteps of Sam Smith, Ellie Goulding and Adele, and all but guaranteeing them success. In March, their single "King" went to number one. They had a triumphant Glastonbury, and their debut record, Communion, went straight to number one.

"It's been a very surreal few months," says Alexander, a thin, gangly 24-year-old with cropped, dyed blonde hair, the palest skin, and an aura about him that might well have him mistaken for a teenager from another decade yet. He is an intriguing mix of introversion and confidence, a singer with a high, pillowy vocal and a catalogue of songs that revolve around a great many bad romances. For all its sonic uplift, Communion is an album riven with the blues. Were the singer not currently in a healthy relationship – with Neil Milan Amin-Smith of Clean Bandit – you'd be moved to feel awfully sorry for him.

"I think I get a kind of morbid pleasure in writing it all down," he says. "I don't write about failed affairs for revenge; they are just snapshots of my life, really. And once I've written it all down, it feels like it's someone else, not me anymore. It's probably healthy."

However, this may not be how the songs' subjects feel about it. After Alexander spoke publicly about someone he liked who had abruptly severed all ties, the unnamed man contacted him.

"He sent me a text but didn't write anything in it; he just sent me a picture of the interview I had done. That was quite a strange meta-experience, and unsettling." He frowns, pushing his fingertips to the bridge of his nose. "I didn't respond to him. I thought it best not to."

Years & Years were formed by Goldsworthy and Turkmen back in 2010. The former is an Australian who had recently relocated to London and was working as a waiter; the latter, originally from Turkey, had been studying architecture. He would go on to qualify, which pleased his mother hugely. She was less pleased when he ditched his prospective career in favour of music. "She always reminds me to say I'm a qualified architect in interviews," Türkmen says, laughing. "She doesn't want people to think I'm a Turk who just came to this country to become a pop star."

The duo hadn't yet settled on the kind of music they wanted to make, though Türkmen was resistant to follow Goldsworthy's impulse to remain slavishly inspired by Marilyn Manson and Nine Inch Nails.

"We didn't have a singer, and we didn't particularly want one," says Goldsworthy, wide-eyed and bushily bearded. "We wanted to be a collective, doing all kinds of music, drafting in vocalists as and when we needed them."

"But then Olly came along," Turkmen adds, "and everything changed." Why, exactly? "We heard him sing."

Under Alexander's direction, the band became, "an analog dance thing". They quickly gained momentum, allowing the singer to at last find his own true identity in the process.

"I always felt like the weird kid at school," he says. "I used to go to classes with eyeliner, Chinese symbols on my face. I suppose I wanted to forge an identity. I wanted to be different."

He was certainly that, and was bullied, identified as gay despite not coming out to anyone. "There was nobody else openly gay at school, so coming out wasn't really an option. But I was weird, so I had to be called something, right?"

He found a kind of refuge in the school's drama room, where the painting of Chinese symbols on one's face was practically encouraged, and felt increasingly drawn to the idea of acting, of becoming someone else. At 17, he auditioned for the Channel 4 teen drama Skins, and at 18 moved to London where he later landed small parts in films and plays, among them an adaptation of Great Expectations and the West End production of Peter and Alice, alongside Dame Judi Dench.

"People think acting is really glamorous," he says, "but at my level it wasn't. You spend three days working on a small film, and the next six months unemployed. I was mostly at home in my windowless room in a tiny flat in Brick Lane."

And so he decided to focus his efforts exclusively on music. Influenced by Stevie Wonder and Pet Shop Boys, he had long been writing songs of a disaffected nature but with rave appeal. He says he has found his true voice now, and doesn't feel quite so weird anymore. But having fans, among them people who may look upon him as inspirational, has had an unusual effect.

"It's weird," he says. "I dreamt about this as a kid – being in a successful band – and so I suppose I am living that dream right now. Thing is, I still feel exactly the same in myself as I did when I was having those dreams. What I mean is, it's not like I've suddenly magically changed into this pop star. I'm still me.

"It's nice to be acknowledged as part of a successful band but when people come up to me when I'm alone and they want to tell me how they feel about me… Well, I find that very difficult, awkward. I think I'm embarrassed about my failure to live up to whatever images they may have of me. I suppose I still feel undeserving of it."

'Communion' by Years & Years is out now