From time to time, a TV show comes along which is so thrillingly original, so wildly imaginative, that you can’t even begin to think where the makers got the idea. Britain’s Best Home Cook (BBC1, Thursday) isn’t one of them. Nevertheless, it has a serious claim to being the most important new programme of the week — if only to the BBC which, despite the failure of The Big Family Cooking Showdown (whose title I just had to check via Google), clearly hasn’t given up on the possibility of finding a way to replace The Great British Bake Off.

But in fact there’s another series that some viewers might feel is lurking in the background here — and that’s W1A. For the past few months, BBC pods have presumably been full of BBC bods discussing how much Britain’s Best Home Cook should stick to the conventional formula and how much it should ‘refresh’ it. Their conclusion, not surprisingly, seems to be that they should keep the refreshment to a minimum, but make a big fuss about any mild innovations even so.

In one excitedly announced twist, for example, the cooks have to live together in the same house, but just in case that’s too daring, we don’t see them there much. Other radical developments, meanwhile, are having the kitchen areas in a semi-circle rather than rows, and ending each episode with the culinary equivalent of a Strictly dance-off.

Apart from that, it’s very much business as usual, with a scrupulously diverse selection of competitors, a deep commitment to overusing the word ‘ultimate’ and Mary Berry twinkling away as one of the judges.

The presenter, somehow inevitably, is Claudia Winkleman, who’s already perfected the key tactic of repeating exactly what any contestant tells her, except in a tone of utter incredulity. The first challenge was cooking ‘the ultimate burger’, and one woman explained that hers would be made of prawn and beef. ‘Prawn and beef?’ gasped Claudia, with an unmistakeable ‘WTF?’ left unvoiced — although this was as nothing compared with the almost unhinged extravagance of her ‘You’re making your own burger cheese?’ when faced with someone making their own burger cheese.

For their part, the contestants also knew what was required of them, especially when it came to the fearless deployment of national stereotypes in their food. Obviously, this is easy enough for people of an Asian or African background, but what if you’re from Wales? Katie, born and bred in the Valleys, didn’t hesitate. ‘I’m making a Welsh rarebit cheeseburger,’ she revealed proudly, before breaking off to chop some leeks for her coleslaw.

On the whole, Britain’s Best Home Cook does achieve the necessary warm-heartedness, with the ten participants making a rather convincing case for we’re-all-Brits-together multiculturalism. The final cook-off between the candidates for expulsion, while no Cuban missile crisis, also adds a note of genuine tension. The only trouble is that at this stage in television history, everything about the programme is so knowing that everybody involved seems not so much to be taking part in a cookery competition as re-enacting one.

The cast of BBC1’s new drama The Split (Tuesday) is female-led — although to save time, from now on can you just assume that every TV-drama cast is female-led unless I specify that it’s not. (Can you also assume that all of them will be greeted by newspaper articles delighted that a TV drama has a female-led cast ‘at last’.) Nicola Walker stars as Hannah Defoe, a divorce lawyer who’s left her mother’s divorce-law firm to work for a rival — and to amplify the show’s central theme, which is the fragility of families.

Otherwise, there’s really no avoiding the word ‘glossy’ here, as lots of well-polished people exchange lots of well-polished dialogue in various glittering London locations — or, failing that, while striding down corridors at a brisk 5mph. The clients are a pretty glamorous lot too, with Tuesday’s episode bringing us the negotiations for a pre-nup between a top footballer and his model fiancée.

At the heart of the programme, though, is Hannah’s relationship with her two younger sisters: rackety Nina and sweet young Rose. Despite that central theme, the relationship seems pretty solid to me — without ever being idealised. Instead, in a feature not unknown in families, the sisters can say the sort of home truths to each other that would destroy most friendships, but in this case are barely enough to distract anybody from their champagne.

Yet, for all its qualities — which certainly include being highly watchable — I’m still not sure the show has quite decided what kind of drama it wants to be: high-class soap-opera or thoughtful meditation on the nature of family life. In theory, of course, it’s possible to be both. In practice, The Split is so far shuttling a bit uneasily between the two.