She speaks as rapidly off stage as she does on it – “I just keep talking until someone tells me to stop,” she says laughing – and her thoughts move fluently from one subject to another without pause. “So much happened in my life,” she says. “There were two deaths in my family in quick succession and I went through a big, messy break-up.”

But even when she was miserable, Suzi turned up for her gigs. “The weekend my Nan died and I broke up with my girlfriend, I went on stage and talked about it. But everything I do on stage comes from my life – I sometimes wonder if I’m revealing too much – and when I was heartbroken I did question how many times I could go on stage and talk about it. But I think the best stuff I’ve written is where I’ve had a visceral response to something, and hopefully people will connect with that.”

The emotional events fed into Keeping It Classy. “It was supposed to be entirely about class – how I had become this avocado-munching-yoga-practising Londoner, but when I began to write it, it also became about how I was recalibrating my life. The deaths really affected my family, and I was with my girlfriend for four years and we were engaged; I thought my life was going in one direction, and then that changed.”

Suzi, 32, comes from a close “large, loud, rough-and-tumble, a bit dodge in the nicest possible way” family. Her dad buys and sells lorries and, after raising Suzi and her older brother, her mum became his assistant. The comic was the first in her family to go to university, while her 24 cousins (“Christmas is mad”) all do what she terms “proper jobs” – working in pubs, waitressing, scaffolding.

She used to bunk off school. “I wasn’t clever and didn’t have friends. I had a chip on my shoulder because I was gay and I was keeping this big secret, so I was just a ball of anger, and I think my teachers just gave up on me.

“I went to a school where a teacher might not even turn up. So I thought if I wasn’t worth teaching, it wasn’t worth having ambition. Ambition wasn’t instilled in us at school – it was my mum and dad who encouraged me.”

By contrast, she reflects without rancour but with the analytical mind of a social observer on the time a fellow comic took her to his old Oxford college. She was wowed by the magnificent buildings in which he had studied – incidentally, where some of the Harry Potter movies were filmed. “I thought, of course if you went here you would believe anything is possible with your life.”

Even as a young child, she knew there was currency in being funny. “My Dad and my uncle would tell stories in the pub and everyone would listen to them and I loved it. I sort of knew being funny was better than being good [at school].”

Joining a youth drama group transformed her outlook and she decided she wanted to be a comedic actress – Victoria Wood, French and Saunders and Catherine Tate are her heroes. She later attended drama school in London and it was there she first did stand-up, “I felt really comfortable on stage as me, not in character” – and decided this was where her career lay.

She worked hard at learning her craft, driving all over the UK for club gigs, studying more established performers and honing her material. Since starting in comedy full-time in 2012, Suzi has supported several big-name comics on their tours, including Josh Widdicombe, Romesh Ranganathan, Alan Carr and Tom Allen, and now Keeping It Classy is her first headline tour.

I ask what her fanbase is. “My audience is broad, I think; people who’ve seen me in clubs or supporting other comics, gay men and women, and quite a few teenage gays who come with their parents. I’m a safe bet for families – I can be a bit cheeky on stage but not coarse. My general rule is I have to be able to say it in front of my Mum and Dad.

“I never try to be shocking or unnecessarily mean. I never punch down or take the piss out of working-class people. I don’t think anything I do is particularly contentious but I think audiences like me taking the piss out of them.”

Among her audience are fans of Like Minded Friends, the podcast she has been doing with Tom Allen for the past 18 months. “It has become way more successful than we thought,” Suzi says. “It’s not just for gays, it’s for everyone. A lot of gay stuff in the media is downbeat – Aids, homophobia, discrimination – so Tom and I thought we would talk about the joyous things, to celebrate who we are.”

Keeping It Classy had a sellout run at the Edinburgh Fringe last August, and Suzi has updated sections of it, including Brexit, which can divide the room, but which she tackles nonetheless. “I’m still angry about it, but lots of my family voted for it and I understand why,” she says. “But you have to find ways of making even such a divisive subject funny – and I don’t want my act to be a TED talk.

“I mean, I want people to think, but I want them to laugh more. Actually, I just like buggering about on stage.”