The scattershot sketch show with the odd musical number continues, and while Ullman's portrayal of Judi Dench as a compulsive hellraiser insulated by her national treasure status is a solid, repeatable gag, it almost overshadows her impeccable impersonation of Maggie Smith (here reimagined as an eager-to-please YouTube vlogger). Elsewhere, Nicola Sturgeon goes to great lengths to get the Angela Merkel look.

Although sketch shows are naturally dilettantish, Ullman's skims too many surfaces. The impersonations - Maggie Smith, Germaine Greer - are on the money and skits such as the one about greetings cards all being rude nowadays are solid, but it's all a punchline or idea short. Observations on gentrification and posh actors lack a fresh point, and a playlet about a woman thwarted by her elderly mother hasn't time to develop its pathos.

Review of the week: Tracey Ullman's Show

I might sound like a grumpy old grandad who's out of step with everything that's cool and trendy but really: what's all this fuss about Tracey Ullman?

Tracy Ullman on why Monty Python 'p****d her off'

Tracey Ullman said she tore into Michael Palin over Monty Python's all-male line-up when they first met. The actress, 57, said: "Python used to p*** me off when I was young. When I met Michael I said, 'Why did you never have women in the show?' He was so adorable and said, 'I think we were rather frightened of them' - so it was easier for Terry Jones to do it."

The sketch show returns with our Tracey as adept as ever at playing a range of characters. Prepare for a delinquent Dame Judi Dench, a Bond-villainesque Nicola Sturgeon and Clare Balding's need to present every TV show going ("I just want to help!"). But the best sketch by far makes grotesques of Jerry Hall and Rupert Murdoch (Ben Miller) at a painfully strained family dinner - more risks like this, please.

Tracey Ullman's guide to her favourite impressions

Veteran comedian Tracey Ullman takes RadioTimes.com through her celebrity faces - Judi Dench, Nicola Sturgeon Angela Merkel, Germaine Greer and The Murdoch Bunch.

Preview: Tracey Ullman's Show Series 2

Overall, the strike rate, upped with some hit-and-run quickies, is impressive. Tracey Ullman's Show could be that most elusive of things: a primetime BBC One show that pleases critics as much as audiences.

Tracey Ullman interview

The veteran comedian is back - but how does she get inside the characters who make us laugh?

Tracey Ullman's Show review

Ullman throws herself at it with gusto and it's iconoclastic enough to elicit gasps as well as giggles.

Preview: Tracey Ullman's Show Series 2

As you would expect, there are some great new characters introduced in the second series.