Dan Smith doesn’t know how to switch off. In the decade or so that he has been the creative heart, and frontman, of the band Bastille, he has thought about music constantly. There was a two-week period over Christmas and new year where he thought he had managed not to. Then he went to a double bill at the cinema.

“I got the whole way through the first film and three-quarters of the way through the second film before I had to leave, sing into my phone in the corridor awkwardly, and then come back in,” he says. “If I have a song idea that pops into my head, I have to get it down. It will eat away at me if I forget it, or it’s just on loop in my head.”

This may be testament to Smith’s catchy hooks. Since the release of Bastille’s first album, it has been a decade of No 1s, award nominations and sell-out tours. Commercial success was swift, although critical acclaim followed more slowly. A fourth album, Give Me the Future, is released next month.

Yet, despite this objective success, sitting in the control room of Bastille’s studio with his ankle resting on his knee, Smith says he has a “very low opinion” of himself. “I can’t really explain it,” he says. “I think there’s dissonance in my head between what we’ve achieved and how I’m perceived, and the reality in my head.”

Smith, 35, is impossible not to like. We speak twice, first over Zoom before Christmas when he is isolating with Covid at home, then in the unassuming studio building, tucked behind a car showroom in south London. After greeting me, he is away, chatting freely about parties with his university friends for New Year’s Eve, “hangxiety”, insomnia, diets and how much he loved spending Christmas with his family (especially his young nephews), often interrupting himself with overlapping tangents, his broad hand gestures to emphasise points. He is affable, funny – and touchingly hospitable (“I’m sorry if you think I’m trying to drown you,” he says after offering to get me water for a fourth time).

When he talks about the pressures of being in a band – touring, criticism, fame, performance anxiety, onstage panic attacks – he does so with humour and an explicit caveat about how privileged he is to do what he does. With his fastidious modesty and painstaking self-awareness, he is very much the millennial frontman.

“I’ve never been good at trying to pretend to be like this slick, rock star frontman, because it’s not what I ever wanted to be,” he says. “I see other artists who are so good at that – and it’s a skill in itself – but it’s just not one that I’m that interested in.”

Smith isn’t keen on interviews or photoshoots (“Just to warn you, I have no control over my face,” he says, deadpan, approaching the photographer). He seems at ease today, although he tells me his university friends still find it hilarious that someone as introverted as him is the lead singer of a mainstream band.

Smith grew up in south London with his lawyer parents and sister. He had a happy childhood, he says, but he was a self-conscious child and never dreamed of a musical career. “Just the idea of standing up in front of people and doing anything, let alone playing music, was so far from anything I could imagine wanting to do.”

As a teenager, Smith wrote songs on his piano and laptop in his bedroom, but kept them to himself. Then, at university, friends encouraged him to join a talent contest (he was runner up). Pub gigs and open mic nights followed, but he experienced severe stage fright. “I was so nervous. I was such a wreck,” he says. “I used to drink quite a lot before going on, which was not conducive with having to hit a loop pedal and keep time with yourself. It was a nightmare.”

In 2010, after finishing university, Smith formed Bastille with Chris Wood, Kyle Simmons and Will Farquarson. The band released an EP independently and built up a loyal following, touring the country in borrowed cars. The band’s first album, Bad Blood, was written in Smith’s bedroom and produced with a friend. “It couldn’t really have been more DIY if it tried,” he says.

Even when they signed a record deal he never thought they would be successful. “We were never hyped; we weren’t being told we were going to be successful. So it was news to us. It was news to our record label, and to everyone!”

But when Bad Blood was released in 2013 it debuted at No 1 in the UK albums chart and became the biggest-selling digital album of that year. Its anthemic earworm, Pompeii, went platinum in the UK and double platinum in the US. Critics hated it.

“It was rinsed!” Smith says, laughing.

“It’s such a cliche, but you can hear 100 nice things and you remember the one that’s not. It’s such a human thing. And maybe it’s an anxious-person thing to fixate on the negative.” Critics were kinder to later albums Wild World (another UK No 1) and Doom Days (which peaked at No 4 in the UK), and in 2015 the band were nominated for a Grammy.

But this intense, sudden rise to fame “freaked out” the fame-averse Smith, who is happy with the fact that many people have heard Bastille’s music, but have no idea what he looks like. “I was hugely self-deprecating as a defence mechanism,” he says. “I was always such a huge pessimist. We all worked so hard on the band at the beginning – and continue to – because we loved it. But I’ve always been expecting it to fall apart at any moment. I think that’s why I never think too far in the future.”

Smith has a complicated relationship with his appearance, partly, he thinks, from being overweight as a teenager. “I was big through the end of childhood and through quite a lot of university,” he says. “I’m really aware of not wanting to imply that anyone shouldn’t want to be big. But I remember being just really self-conscious and wanting to look different.”

Before his third year at university, he went travelling in Thailand and caught a virus. He lost his appetite and the weight fell off. When he returned home he started eating more healthily and exercised more. That summer, his weight dropped six stone. “When I lost loads of weight and suddenly just looked like a different person, it’s quite a … I think for anyone that’s gone through quite a big, radical physical transformation it can be a fair thing to get your head around.”

He doesn’t want people to think this was a magical or aspirational transformation. “It didn’t suddenly instil me with loads of confidence,” he says. “For a long time, I still identified as a bigger guy, and still do to this day.”

Smith says he has never felt pressure from the music industry to change his weight, but his body dysmorphia meant the constant exposure to seeing his own face – in videos, photographs or artwork – has been tricky to navigate. “It’s a bizarre line of work in which you are constantly confronted by your own image,” he says. “It’s not fun – and it doesn’t feel particularly healthy.

“I think a lot of people suffer from different versions of body dysmorphia,” he says. “We all have the version of ourselves that we see in our own heads and often that’s so different from the version of who we are through other people’s eyes.”

It makes being on stage uncomfortable. “For someone who has body image issues, it’s complicated getting up on stage every night in front of lots of people, when your instinct is to hide away,” Smith says. “Sometimes it’s not a problem, sometimes it is.”

Smith has never needed to drink before getting on stage to perform with Bastille, but it is still a nerve-racking, isolating experience even with his bandmates beside him. “It’s really up in the air as to whether or not I’ll have a good show or not because I get really nervous,” he says. “I have this really unhelpful thing where I go pitch deaf on stage – so I can hear noise, but can’t place anything – and then I become really self-conscious about not singing in tune, because you can’t hear what’s going on.

“I remember playing at Alexandra Palace [in north London] – which should have been such an amazing moment – and two songs in I just lost it and went completely pitch deaf and the whole gig for me was then this mad, terrifying rollercoaster of just trying to get through it. I hear myself saying this and it’s just a real shame.”

Performing, in other words, is what he has to do to fulfil his passion of writing, recording and working with other creative people. He wishes he could enjoy it, and is honoured that fans come to see him, but his stage fright is “essentially a form of a panic attack”.

Bastille’s fourth album leans heavily into Smith’s fondness for sci-fi (he talks fervently about the films Brazil, Minority Report and Ghost in the Shell, and the writers Philip K Dick and Margaret Atwood). He made his directorial debut for the music video to No Bad Days, exploring themes of resurrecting loved ones through technology. The song was inspired by Smith’s aunt, who died of cancer a few years ago.

“She happened to live in a state in Australia where they just legalised assisted dying and she was one of the first people to go down that path,” he says. He was able to travel to see her before she died. “To me, she’s amazing for having taken that decision and was so amazingly generous at helping guide all the people around her that she loved through this incredibly difficult situation.”

In the past 10 years, Smith has rarely taken time off. Even during lockdown last year he didn’t slow down, spending his days finishing the latest album, running an online film club and volunteering at food banks and vaccination centres. In the evenings he wrote more music, like he did as a student (“which I loved”).

And when he’s not with Bastille, Smith is collaborating with others and enjoying being “a small part in this much bigger thing”. He has written songs for artists (including Yungblud, Lizzo and Haim); scored films (his latest is the upcoming From Devil’s Breath, a short film produced by Leonardo DiCaprio), and worked with other musicians through Bastille’s record label and studio, One Eyed Jack, which the band set up to offer a free space for other (often emerging) artists to use. He is also co-hosting a BBC Sounds podcast with books enthusiast Simon Savidge, Turn Up for the Books, out this week, and is working on a full-blown musical with two of his friends. What does he do to switch off? Marathons, naturally.

Doesn’t he worry about burnout? “Massively!” Smith says. “But I think because we started in a place where I was involved with every single bit, and was determined to not leave that, I’ve just stayed involved in everything to the point where it can be consuming. I think, at points, I’ve just taken on way too much.”

With all the success that Bastille has experienced, has his “brutal critical narrative” quietened down? “I think there’s a small part of me that’s really, really conditioned to think that way,” he says. “But I think I’ve seen some of that negativity beaten out of me by the fact that it’s 10 years on, and we’re still allowed to do this stuff.”

And as long as he’s able to keep doing it, he is happy. “Recording has always been the thing I do for fun,” he says. “The studio is the bit I love. Touring and all the other things that come with being in a band are just a side point to making songs, writing songs and creating something out of nothing. Which, for me and my basic little brain, is really satisfying.”

Give Me the Future is released on EMI on 4 February. Bastille tour the UK in March and April. The Turn Up for the Books podcast is on BBC Sounds from 12 January.