I was told to get in the trenches and cut back on the comedy godzillas by a reader recently so I made a trip to the the Invisible Dot's new regular Saturday Night Show last night. I'm not sure if this really counts as the trenches though. It's a swish, industrial room a spit from King's Cross station which attracts the coolest of comedy crowds (think Hacienda Club just before acid house kicked in but cosier) thanks to ID's skilful booking policy. In the past they have promoted gigs by the Daniel Kitson, Tim Key, Stewart Lee. They certainly know what's what and what's new, and have their ears on the pulse, fingers on the ground, all that sort of thing.

First on the bill – not bottom, note, just first because he had another gig to go to – was fearless immersive character comic Adam Riches. It is getting on for two years now since Riches won the Foster's Comedy Award so maybe it is about time that he started a develop some new material, but when his material works so well who can blame him for still dragging his audience out of their seats to take part in yet another game of extreme swingball.

As for his failsafe Daniel Day-Lewis sketch, it is not no much an impression as a widescreen hyperbolic satirical demolition of method acting, as he deconstructs the Oscar-winning thesp's style, hauling a member of the crowd up the reenact a scene and asking them to use "Passion and conviction: Two words that could easily describe my first marriage." The short set ended with Riches and fan grappling on the floor next to a pile of cardboard boxes, a typical in-your-face finale for this fearless funnyman.

Riches is a tough act to follow and James Acaster's dweeby, reserved style could not be more different. But his Foster's Award nomination last year seems to have given Acaster's confidence a leg-up and this was the  best performance I have seen from him, even if he did miss out some material which meant that he could not deliver some planned callbacks later on. This didn't really matter as Acaster is so naturally funny and likeable that explaining that he had fucked up was funny enough anyway. Maybe he should keep the mistakes in.

There were some good jokes here too, such as his business plan for selling ice creams  with unlimited refills as long as you can resist eating the cone and his method for remembering where to place the balls when setting them up for a game of pool. Acaster has a penchant for rhythmic comedy as anyone who has seen his "Kettering" chant routine will know and there is more of that here, alongside a discussion about the futility of questionnaires and a highly amusing skit in defence of Yoko Ono.

It is an indication of how lovely this club is that as Acaster left he said that he now had to play to a "bunch of dicks in Covent Garden." I guess if I really wanted to get into the trenches I should have donned my helmet and followed him, but instead I stayed for the great Daniel Simonsen. The Norwegian stand-up won the Best Newcomer Award at Edinburgh and, like Acaster, has an instantly winning laid-back personality that just makes your face break into a smile as soon as he walks onstage. Well. I say "walks onstage", his entrance actually involved scuttling through the crowd and asking me to move my chair so that he could squeeze past me – the venue is that cosy.

Simonsen's act is a heady cocktail of self-analysis and self-loathing. There are few comedians working today who are so clearly riddled with doubt and insecurity and yet at the same time are so good at what they do (Simon Amstell, who Simonsen has supported, is the only other one that immediately springs to mind, so maybe it is infectious). As Simonsen explained as he anxiously scratched his head, he decided to try stand-up because he had difficulty talking to people. It's one of the weirdest aspects of this art form that you can address a room of strangers and be the centre of attention but have difficulty buying a train ticket at the station.

There were plenty of deadpan gags between the angst as he explained why comedy is hard to do in Norway: "When a joke doesn't work they really laugh." Last time I saw Simonsen, at the Soho Theatre, he ran out of material after 42 minutes. No such problem here in this short, sharp set that blended the old favourites – claiming benefits abroad because you might as well see the world when unemployed, recalling the time he had to dress as a tooth for work – with new work-in-progress riffs.

It is no surprise that Simonsen – like Dr Brown – has studied clowning, he has a very subtle physicality, particularly when mimicking the way people dance in South America.  Stardom clearly beckons. He is soon to appear in Reeves and Mortimer's new BBC sitcom, Vic and Bob's House of Fools. Simonsen plays Bob's Norwegian son Erik. Vic and Bob have a terrific track record in spotting talent, most recently Matt Lucas and Dan Skinner (aka Angelos). I think they've done it again.

The Invisible Dot's Saturday Night Show is every, erm, Saturday for the next six weeks, but pretty much all of the Invisible Dot's shows are worth seeing. Details here.