Miles Jupp, London Palladium

Miles Jupp starts by telling us he’s trying to fathom the kind of comic he should be, after he overheard a comment by an audience member at a show on his previous tour: he was nice, the man proffered, but what he said had taken him by surprise. So should Jupp now be full and malice and predictable?

The answer, without spoiling it for you, is no. Instead Jupp is his usual gentle and fogeyish self that listeners to Radio 4's News Quiz, which he hosts, television panel shows on which he regularly appears, fans of Rev and The Thick of It, and those who have seen his previous stand-up shows, know and love. And while talking down his own fame by describing awful appearances on "celebrity" versions of TV shows, he gently guys his audience, who “wear several shades of beige” and are devotees of Waitrose.

In the section on Duchy Originals biscuits we see a steelier side of Jupp

Songs of Freedom is an untroubling meander through life’s vicissitudes – or rather the vicissitudes you suffer if you’re sort of famous but not quite a celebrity, have a wife who has a laissez-faire attitude to the placement of objects in the family home and are the father of five children who can’t wait for the school holidays to finish so you can have a rest.

In an underpowered first half, Jupp tells a few long-form stories (some of them may be true), that rely on that bumbling mild-mannered bloke persona – my goodness, he’s even looking forward to having a nice soak in a hot bath after this jolly old nonsense in a theatre has ended. He describes his horror at being mistaken for a trainspotter, what he puts in his children’s lunch boxes and his clothing choices for a long journey. These stories – with tiny, nicely observed details that slowly build a forensic picture of Jupp's life – while amusing, never quite get to a punchline, The effect is indeed like wallowing in a warm bath, but at times we might like a brisk cold shower, too.

The second half, thankfully, picks up pace, and we see flashes of the angry Miles, the one whom he says he is barely able to keep in check, as evidenced by his young children repeating some of daddy’s more, er, interesting phrases to describe broken boilers or broadband technicians who never turn up when they’re bloody well supposed to. He also neatly stabs the odd celebrity – Richard Madeley, Alan Yentob, Nicky Campbell – with the briefest of asides or the subtlest of putdowns.

But it's only in the section on Duchy Originals biscuits that we see a steelier side to Jupp, and one that I would have liked to see more of. It's a superb piece of writing; he says the Waitrose favourites are not just overpriced (while acknowledging their deliciousness), but he also explains why we are paying twice – skilfully making a case for a republic in this most polite of diatribes. Let them eat biscuits…

• Miles Jupp is touring until 25 March
• More comedy reviews on theartsdesk