Psychobitches, Sky Arts 1/ Up the Women, BBC One

Unfortunate title aside, Psychobitches is a wonderfully original idea - what if famous women through the centuries were alive today and seeking treatment from a psychotherapist? In a quasi-sketch format using the talents of 10 credited writers, it's a neat construct that allows writers' imaginations free rein, unconstrained by time, place or actual facts, and gives a roll call of talented actresses (and the occasional bloke) a chance to do their very best impersonations.

Last night's opener of a five-part series (expertly directed by The League of Gentlemen's Jeremy Dyson) started with Rosa Parks, not on the couch but “here for my appointment” in a glorious blink-and-you'll miss-it sight gag, where all the other women in the waiting room jumped up to offer her their seat. Actually being therapised, as it were, in the Sigmund Freud-style office, were (among others) an irritatingly winsome Audrey Hepburn (Sam Spiro), a grandiose Eva Peron (Sharon Horgan) and a self-obsessed Sylvia Plath (Julia Davis).

Plath was trying out a new writing persona in which she donned her grandmother's dress and wig and morphed into Pam Ayres - “I wish I'd looked after me toes/ Not treated them like they were foes” - one of many moments in this half-hour when I laughed out loud. It was an inspired gag. Equally good were the scenes involving the bickering Brontë sisters; Anne (Sarah Solemani) was meek but knowing, while Charlotte (Selina Griffiths) was withering about Emily (Katy Brand) needing to lose her virginity, or, as she put it in her broad Yorkshire vowels, “She should fuck off to Keighley on a Friday night and lose it to a cowhand and do us all a fucking favour.”

Among the mix was Mark Gatiss and Frances Barber hamming it up marvellously as Joan Crawford and Bette Davis, in full What Ever Happened to Baby Jane? mode, endlessly outdoing each other in the meanness stakes, while Rebecca Front's therapist - an unshowy part that could easily go unnoticed in this parade of misfits - was nicely pitched. There was the occasional miss, but overall this was a joy.

Rebecca Front was also to be seen in Up the Women, written by Jessica Hynes, who co-penned the rather brilliant Spaced (1999-2001) but who, strangely, has never received the same acclaim as her co-writer Simon Pegg.

Up the Women is traditional in its format - it’s set mostly in one room, in this instance a village hall where the Bunbury Intricate Crafts Circle meet. It’s 1910, and one of BICC’s members, Margaret (Hynes) has been seduced by Suffragettism while on a day trip to London. The group's self-appointed bossy-boots leader Helen (Front, pictured far right with Hynes), meanwhile, is having none of it when Margaret meekly suggests the group might support women’s emancipation - “Women should not have the vote. We are simple, emotional creatures.”

Margaret is a brainy woman who has long since accepted that women must always defer to men, even those markedly less intelligent, and a good running gag involved her explaining electricity to the overbearing caretaker (Adrian Scarborough), who was struggling to fit a new-fangled lightbulb.

The characters - particularly Vicki Pepperdine’s toothy spinster - are drawn in broad strokes, and occasionally the humour (peonies being misheard for penis, for instance) is groaningly obvious. But there are some neat lines too, and superb acting from a fantastic cast who look like they’re enjoying themselves, including Judy Parfitt doing a nice turn as Helen's decidedly naughty mother, Myrtle, sexually liberated long before the term was invented by the Pankhursts’ spiritual daughters. Worth staying with.

• Psychobitches and Up the Women continue on Thursdays