'I think I can draw both a mainstream audience and an alternative audience to my shows,' says James Acaster as I ask about his increasing fanbase. 'I also have the ability to disappoint both.' Over the last six years, the Kettering-born stand-up has steadily become one of the biggest names at the Edinburgh Fringe. He fills larger venues each year, his six solo hours have garnered dozens of glowing reviews and the last four of those shows received nominations for the top prize in live comedy, the Edinburgh Comedy Award.

But that doesn't mean the Edinburgh Fringe has become routine for James Acaster. With bigger crowds, increased TV exposure and heightened expectations come greater challenges. 'If someone's seen me on Mock the Week and expects me to be like Michael McIntyre, then they get annoyed when I start the show on my knees,' says Acaster. 'And if someone comes because of critical acclaim and nominations, then they get annoyed when I do an observational routine about massage: "What the fuck is this? This is just normal comedy!" I can annoy purists on either side.'

But those are the extremes. Acaster's also built up a large, loyal following who can't get enough of his quizzical, fanciful stand-up. The 31-year-old comic has spent years defining his persona and perfecting a style, and his intricately written shows usually feature a relatable truth masked behind mischievous, fabricated tales about being an undercover cop, for instance, or the biscuit-eating habits of Yoko Ono. 'I'm almost able to be more honest by lying,' he explains. 'By making everything up I'm able to say what I really want to. It's all based on truth – on something I actually feel or think – but I package it in a different way to get the laugh through more.'

That hasn't always been Acaster's tactic. When he started performing stand-up on the open-mic circuit in 2008, he regarded dishonesty as cheating. 'I thought: anyone can make up a lie, but making the truth funny is really hard. But I actually had more problems with people believing me when I told the truth on stage.'

Acaster's early Edinburgh runs weren't plain sailing, either. Audience numbers were low for his second show, Prompt, until it was nominated for the Edinburgh Comedy Award, and his third solo offering, Lawnmower, was a particularly taxing experience. 'People don't put pressure on you for the third show,' Acaster claims, 'and actually it's a lot more stressful. You think that you now know what your pattern and method is, and no one tells you that every year is different. I thought that there was going to be an expectation on me because of the nomination, but there wasn't: that's all in your head. So I had a year of thinking: everyone's going to think last year was a fluke and this is shit.'

Three Fringes (and three more award nominations) later, and Acaster is a lot more relaxed about the festival and looks forward to it more each year. 'You realise you enjoy coming up with new material and saying new things on stage, and when you realise that, it's just great. I'm really not doing it for any other reason.'

Another reason? Those award nominations, for instance? Acaster doesn't have much to say about his four gong noms. 'It's very nice,' he manages. 'That's it, really.' But he must feel something about being officially namechecked as one of the best comics at the Fringe for four years in a row? 'It's really nice that four groups of people have said that,' he elaborates, slightly. 'But I do believe that if you took a different group of panelists each year there's every chance that I would have never been nominated.'

Acaster is the first comedian to have ever clocked up four consecutive nominations. Surely he must feel pressure to win the thing this year? 'No one is going to base their opinion on me from what happens with the awards this year,' he reckons. 'Last year, people thought I was going to be disappointed about it [not winning]. To me, that'd be insane. People asked, "Are you OK?" and I was like, "I've been nominated four times! What are you talking about? Who gets nominated four times and then gets grumpy about it?"''

Being an Edinburgh Comedy Award nominee has helped put bums on seats in Edinburgh, he admits, but it's hard to say whether it's made much more of an impact on his career. 'The first time I was nominated it definitely didn't help. The Melbourne Comedy Festival rejected me, I couldn't sell my tour, I couldn't get on any TV shows. It definitely didn't help me then.'

These days, of course, Acaster has achieved all of those things and more. After this year's Fringe, he's taking the new show, Reset, on tour including dates in Glasgow, Edinburgh (again) and Aberdeen. After pretending to be an undercover cop in 2014 and tales of jury service last year, Reset is the third in a 'sort of trilogy', says Acaster. 'The show is about how I'm set to go into the witness protection programme and about how we all want a fresh start in life. It's also about something else, a personal thing, my own reasons for wanting a fresh start. So it's a crime-themed trilogy that is actually all about uncertainty. And it's the third one that begins with "re".'

After six years of Fringe success, it must become easy to take sell-out shows and critical acclaim for granted. But for James Acaster, he's constantly grateful for his success. 'Every year in Edinburgh I end up waiting behind the curtain about to go on stage and I have a moment of thinking: no one's told me what to do with this show, I've done exactly what I wanted. This is the biggest arts festival in the world and all these people have shown up. Aren't I lucky? It really is amazing.'

James Acaster: Reset, Pleasance Courtyard, 6–28 Aug, 7.30pm, £11–£14 (£10–£13). Previews 3–5 Aug, £8.