To open their first live show, commemorating 25 years of working together, Harry Enfield and Paul Whitehouse enter as the Old Gits. The gag, of course, is that they really are old gits these days. Fiftysomething national treasures, the height of whose fame is long distant, they joked in a recent interview that either may expire before their gruelling tour is done. Certainly, there are moments here when their humour is as creaky as their joints. But it scarcely matters: this is as much about nostalgia as comedy. We’re in the same room as some of the most memorable comic characters of the past quarter-century, so who’s bothered if they generate not so much laughter as a warm, comforting glow?

To be fair to Harry and Paul, some of the creakiness is ascribable to teething problems at this first performance of their tour. Sometimes – as with the uncertain pause before Wayne Slob is visited by the ghost of his deceased wife – the timing is off. Later, there’s a Dragon’s Den send-up which relies on audience participation that Harry and Paul show no sign of yet knowing how to manage.

At other points, the gags land with a clunk that no amount of rehearsal will redeem. A Mr Cholmondley-Warner spoof public information film, Women Know Your Limits, is reimagined to slap down female comedians, which plays awkwardly, partly because of the continuing, tedious currency of that prejudice, and partly because of the power imbalance between our hosts and co-star Catherine Shepherd, playing all the (fairly thankless) female roles. Elsewhere, some jokes are plain weak, like the pairing-up of Enfield’s Kevin the teenager with Grayson Perry (Whitehouse), which is a coincidence of names and not much else.

But even in these flat moments, you’re usually smiling – because the likes of Kevin and Cholmondley-Warner are lovable, on-the-nose characters, and because Whitehouse and Enfield visibly relish reanimating them, together, live on stage. There’s plenty of backchat between the pair (scripted and otherwise) as they tease one another about their accomplishments, their mutual dependency and their decrepitude. The same schoolboy spirit pervades the show, from their clubhouse bores sketch (“is he queer?” etc) to the two urbane surgeons whose portraits are painted, in priapic fashion, by Lucian Freud.

The most successful moments are (only just) more elevated than that, and include Tim Nice-But-Dim canvassing for the Tories and giving his inside track on Piggate, and the 80s favourite Loadsamoney (“I am the son of wad, and I have risen again!”) taking credit for the creation of New Labour. Then there’s Smashie and Nicey reprising the inevitable but enjoyable Operation Yewtree-themed scene Enfield and Whitehouse first staged at a charity gig two years ago.

What’s most striking about the evening is not only the number of indelible characters Enfield and Whitehouse have created, but their efficiency. Distilling personality types, not to mention cultural zeitgeists, into catchphrases this pithy is a form of genius. OK, so it leaves Harry and Paul with characters whose every other utterance can feel beside the point, and with comedy that feels a bit bitesized. Their alter egos get heartier cheers for simply appearing than for anything they actually say, and they seldom hang around for long. But in most instances, it’s an affectionate pleasure to remake their acquaintance.

At Oxford New Theatre, 25 October. Box office: 0844 871 3020. At Cardiff Motorpoint Arena, 26 October. Box office: 029 2022 4488. Then touring until 2 December.