Kevin Bridges, Hammersmith Apollo

Kevin Bridges, an affable young Glaswegian, has had a meteoric rise in comedy. He started gigging at 17, made his solo Edinburgh Fringe debut in 2009, where he played in a 50-seater and earned an Edinburgh Comedy Awards newcomer nomination, and returned the following year to a sold-out run in a 700-seat theatre.

But his real breakthrough was being booked on the BBC's Michael McIntyre's Comedy Roadshow in 2009, which brought him to an audience of millions. His early television success means that much of his material is TV-friendly, but his live shows include more uncompromising material. It's no surprise to learn that Bridges was inspired to go into comedy after reading Frank Skinner's autobiography, for he has that comic's knack of mixing easygoing observational and anecdotal material with some nicely sardonic comedy.

He appears to have reserved his own level of hell for Danny Dyer

The first half hour of Bridge's new show, The Story Continues..., is very strong, with a very well constructed routine about the Coalition's attitude to the unemployed and the current economic situation - “I remember when double dip used to be a good thing”. It's subtle and has a clever payoff, which also provides a neat callback later in the show.

He also has a terrific riff on what the Paralympics meant to him - “Don't worry, I'm not Frankie Boyle” - as he goes into a surreal routine that has little to do with sport but a lot to do with the drug habits of his native city, and Bridges skirts with more danger with references to the dolours of Rangers FC - I thought one guy in the audience was going to deck him – and the pros and cons of Scottish independence.

Along the way he manages to reference Jimmy Carr's tax avoidance - “I want to thank you for paying your hard-earned money to see a comic who won't pay any tax” (he's joking, of course) - watching porn as a teenager with his mates, not feeling sorry for the supposed suffering of the British middle class in these straightened times, and his Scottish brogue being impenetrable to Americans. Bridges is an accomplished mimic and his take-off of various accents is bettered only by his spot-on imitation of Danny Dyer, for whom he appears to have reserved his own level of Hell.

And he may be only 25 but Bridges is an old soul, as his lament about modern chart music – R'n'B in particular – attests. His main beef is that the lyrics, repetitive and vapid as they often are, are “brain-eating”. He has a point and, as he then shows, his irritation comes from a love of words; it's a routine that sadly he doesn't develop. I could have done with much more of that and less of the scatological humour that ended his set, which was certainly a crowd-pleaser but fell short of the comedy that he performed earlier.

Bridges has barely an hour-long show, which these days makes him a part-timer in touring comedy, and on the night I saw him he did an encore that was embarrassingly inept - a Q&A that ended after one question and a refusal to do one of his “I was standing at a bus-stop...” jokes despite repeated loud requests from the well refreshed audience. It was a rare stumble from an accomplished young comic.

• Kevin Bridges is at Hammersmith Apollo until 1 October, then touring UK and Ireland until 8 December