The Catherine Tate Show Live, Eventim Apollo

Catherine Tate's television sketch shows - apart from a couple of specials devoted to her character Nan Taylor - were last screened in 2007, and she hasn't performed comedy live since her early days at the Edinburgh Fringe. So it was particularly good news for fans when she announced her first live UK tour.

Ably abetted on stage by long-time collaborators Niky Wardley and Mathew Horne and co-writer Brett Goldstein, she brings back all the TV series' favourite characters in new sketches. She may have a raft of catchphrases - schoolgirl (“am I bovvered?”) Lauren; gay (“how very dare you?”) Derek; Northern couple (“dirty, evil bastards”) Janice and Ray, et al - but they shouldn't overshadow her gift for characterisation.

In forensic detail Tate captures the nuances of her characters' voices and movement; we all know these people, such as Essex couple Paul and Sam (“what are you like?”), getting over-excited by her describing in grinding detail her day, in which concerns such as running out of milk and a workplace disagreement over chocolate-based biscuits are inflated to matters of earth-shattering importance. So too, do we recognise the passive-aggressive Geordie Georgie menacing her colleague into sponsoring yet another distinctly dodgy fundraiser, and Kate, constantly bullying co-worker Ellen with “go on, have a guess”. (Pictured below, Tate as Nurse Bernie with Goldstein and Horne)

The performers enter and exit the stage with some nicely mannered dancing to pop classics, and the sketches are interspersed with episodic video inserts so Tate can change costume and wig to morph into her next character. We see a sweet love story unfolding between two theatre techies; the outrageously snobbish Aga Saga Woman; the easily scared Frightened Woman; and, most notably, the story that eventually provides the show's denouement. Nan wins a ticket for “that ginger” Tate's live show on Nick Grimshaw's radio programme. The DJ proves himself a good foil in each episode of this very funny story - although maybe no acting was required as my guess is that Tate went gloriously off script during the recording.

Going off script provided some - unintentional - comedy the night I saw the show when Tate fluffed her lines a couple of times and tried to find her way back to the correct cue. She's also adept at audience interaction, as the proud Northern Irish mother “my son's a gay” sketch proves - gently putting down the overkeen fans here, milking the comedy of straight men not wanting to be chosen as her son John's “first boyfriend” there. This interaction gives an unexpected, additional warmth to the show, too.

The lengthy last sketch, where Nan finally enters the auditorium and causes her usual mayhem, is worth waiting for. Nan is a bed-blocking NHS patient who has a brush with mortality and is given a glimpse of the afterlife; Tate and Co give a comic masterclass, with wordplay, audience interaction, crossing the fourth wall and meta comedy. It even ends with an old-fashioned song-and-dance routine.

The live format has magnificently reinvigorated Tate as a performer and - with smart direction by Sean Foley - the show zips along. Allowing for the odd unoriginal joke or crass punchline, this is terrific entertainment.

• The Catherine Tate Show Live is touring until 4 December
• Read more comedy reviews on theartsdesk