There's nothing you can't joke about, say all stand-up comics, but Tom Rosenthal has entered new territory with Manhood – a riveting and often raucously funny show about his circumcision. He is here, he says,  “to avenge the theft of my foreskin”.

John Shuttleworth walks gingerly on stage and stands with his back to the audience. As he points out, the tour – his first in three years – is called John Shuttleworth's Back, and he's contractually obliged to show the audience his reverse side. That is just the first of many exquisitely pedantic reflections from the nerdy Sheffield comic/musician, a character created by Graham Fellows (also the creator of Jilted John and his hit of the same name in 1978).

Scouting and Girlguiding may seem awfully old-fashioned to some, yet many youngsters are still keen to join the Scout movement. Be Prepared (the Scout motto) was inspired by Lucy Porter's two children joining the Beavers, its youngest iteration.

Ahir Shah has delivered some very good comedy by performing as a man who knows he is right about everything – that's what a political degree from Cambridge can do for you. But now the comic, rightly lauded for his previous polemicist shows with two Edinburgh Comedy Awards nominations, is casting around for something other than old ideological certainties to believe in.

Simon Brodkin is best known for his cheeky Cockney wideboy character Lee Nelson, and for pranking the famous – notably handing Theresa May her P45 at the Conservative Party conference in 2017, throwing Nazi-themed balls at Donald Trump when he visited his Scottish golf course in 2016, and, in 2015, storming Kanye West's Glastonbury set and showering then Fifa president Sepp Blatter with banknotes. But now in 100% Simon Brodkin, he is touring as himself for the first time.

It has been seven years since Alexei Sayle last toured, with radio shows and books detaining him elsewhere, but he's back with a bang. As he walks on stage, he immediately starts railing about the “Eton boys running the country”; instead of hailing the school for having produced 20 prime ministers, “it should be in special fucking measures.” Oh, we've missed him.

Simon Evans is a comic known for pithy observational humour, and an often acerbic take on politics, with occasional bits of biography thrown in.

Jen Brister loves her five-year-old twin boys, she is at pains to tell us, even when they have a major meltdown and, like Little Lord Fauntleroys, refuse to eat broken biscuits. Stories like these are sprinkled throughout her new show, Under Privilege, in which she describes trying to instil proper values in children who, she hopes, will probably never know any life struggles, and the broader issue of what privilege is.

David Baddiel is a keen Twitter user, commenting on matters of the day, making witty observations about this and that, or simply chatting to his 650,000 followers. But he does seem to attract trolls, whose idiocy he frequently confronts – and his new show, Trolls: Not the Dolls, was inspired by some of those interactions.

No more glitzy and glam musical shows for Jayde Adams, the comic tells us at the top of the hour. Now, after a few years in the business, she wants to be taken seriously (or seriously enough to host Crazy Delicious on Channel 4), so the sequinned Spandex has gone into storage – “no more camel toes” – and she's popped on jeans and a black turtleneck.