Last month, UK comedy audiences had a visit from Daily Show host Trevor Noah; this month, his Brexit correspondent and so-called “actual British person”, Gina Yashere, follows in his footsteps. Famously, Yashere had to quit Britain and its low glass ceiling for black comedians, to get a break. But this homecoming gig shows she has left in body only. She remains every inch the Londoner, and her set navigates the landscape of British race relations and Anglo-Nigerian manners as deftly as if she had never been away.

And she does so while largely avoiding the stereotypes in which previous routines have traded. This new show Funkindemup finds Yashere on her finest form – prowling the stage, alpha female, effortlessly in charge, at last enjoying the professional status she always felt she had earned. After some ice-breaking gags about rap music, she starts with a section on Windrush, slavery, and the “subtle, side-eyed racism” of the Brits – who are much cleverer than the Americans, says Yashere, at covering their racist tracks.

The content here recalls her Daily Show item on the coverage of Harry Windsor and Meghan Markle’s engagement, as one white person after another expresses innocent surprise that Yashere could possibly be paying a bill or travelling first class. Contrast that – as she then does – with how people look at her in east Asia, which may be racist, or may be confusion about whether she’s female or male. Now we’re in Asia – where Yashere regularly tours – there’s a characteristically pop-eyed routine about hole-in-the-ground toilets, culminating in the deathless punchline: “That’s why when Asians poo, it looks like the emoji …”

If you’re feeling queasy about these ethnic generalisations – well, Yashere is on to you. “I can feel white anuses clenching up,” she beams, before commissioning an Anglo-Chinese man in the second row to play referee. If he laughs, then it’s all right, she tells us – which is, of course, a crude and coercive device (that’s part of the joke), and a lovely way to send up and de-fang any liberal anxiety in the room. Of which there is little, because Yashere is always more ridiculous than contentious, and more clown than social commentator.

Later in the show, we’re treated to Yashere’s account of a dust-up she recently had outside a Washington DC nightclub, and insights into her life as a Brooklyn gentrifier seething at the Jamaican party animal next door. She tries to complain – but her body can’t help dancing. The final section of the show is the most personal, as Yashere discusses her relationship with her African roots, coming out, and her recent experience of introducing a white American girlfriend to her prim Nigerian mother.

I call it personal, and so it is – but none of it feels intimate. Yashere doesn’t give any more of herself away than is required to be funny, and her comedy unfolds along familiar lines, as her mother refuses to hear about Gina’s homosexuality (“I’m walking away!”) and firmly disciplined African kids marvel to hear white friends address their parents by – horror of horrors! – their actual names. It’s the comedy of cultural difference, served up in the conventional way but with no little flair from a woman who has got her career where she wants it – and, on this showing, deservedly so.