I'm a sucker for a chat show. In the absence of Graham Norton and Jonathan Ross I've even started watching Jimmy Fallon and James Corden on Sky to get my fix. But the best of the bunch might be Alan Davies As Yet Untitled on Dave, which returned this week.

It's not your typical chat show. Instead a group of celebrities, mostly, but not exclusively, comedians, sit around a table and shoot the breeze, egged on gently by host Davies. There is no script, no film or tour to plug. They just come to the party – and it does feel like a dinner party without the food at times – and deliver their best anecdotes.

The first show had a srong line-up of Dara O Briain, Angela Scanlon, Sarah Keyworth and Darren Harriott. I don't know how they decide the running order but Harriott went first with a vivid tale of drugs and embarrassment on his first trip abroad, to a festival in Croatia. The Black Country comic is great storyteller and everyone around the table was hanging on his very word.

Sarah Keyworth's story gave Harriott as run for his money as she talked about wearing a suit at a wedding in Ireland. The problem was finding a suitable suit for the occasion and in the end she settled for a boy's outfit. It was a version of a story I've seen Keyworth talk about onstage but that didn't really matter. Few people will have seen her tell it before and it was perfect for the occasion, teeing up her self-deprecating but sharp personality nicely.

I did wonder if Dara O Briain had been held back in the running order because his effervescent wit would have been a tough act to follow. Angela Scanlon and O Briain had a great comic exchange about traditional Irish dancing. Apparently he's quite a mover, though he didn't go as far as to get up and do Riverdance on the table.

While some Dave shows feel a little stretched at an hour, As Yet Untitled is a breeze and leaves you wanting more (there's an extended podcast version to sort that out here). Future guests include Harry Hill, Richard Ayoade, Joe Lycett, Guz Khan, Joel Dommett, Bill Bailey, Sara Pascoe, Desiree Burch, Harriet Kemsley, Adrian Edmondson, Joanne McNally, Jason Manford, Rosie Jones and Lee Mack.

Davies is the perfect host because he doesn't do much. But that's a skill in itself – and he always has plenty of stories up his sleeve if the conversation calls for them. I doubt if he'll ever get to be the host of a primetime chat show but maybe this is more fun. As well as needing less preparation.