Since the big announcement, it’s hard to think of Jodie Whittaker as anything other than the Doctor, waiting in the wings. First, though, she’s playing just A Doctor, in Trust Me (BBC1). Or rather Not A Doctor, because she is not a doctor; she’s just pretending to be one. No, not because she’s an actor. She is an actor pretending to be not a doctor pretending to be a doctor, got it? Trust her, she’s a fake doctor.

Cath starts out as an overworked, underpaid ward sister in a Sheffield hospital. She thinks about leaking some of her concerns about negligence and care (patients left for hours in soiled bedsheets, not getting enough food and water) to the press. But the local paper will only run the story if she is in it. “A story like this lives or dies on a personal angle,” the reporter tells her. Really? What kind of rag is the “Sheffield Express”, and why do they not understand how whistleblowing works?

Anyway, Cath decides against it; she’s a single mum, too, she needs her job, so she takes her worries instead to her own hospital trust. And gets fired for her trouble. On top of that, her best friend Alison, an A&E doctor who’s had it with the NHS, is moving to New Zealand to become a sheep farmer. What’s Cath going to do?

Well, as it happens, at Ally’s leaving do, Cath comes across a manila folder with all her friend’s paperwork – CV, degree, certificates, doctor’s identification etc – in the bin (Ally really hated the job, sheep farming is the future, there’s no going back). So Cath takes it. Well, Ally did say to take anything – “and I mean anything, it’s yours”.

She gets a few books – Medicine The Speedy Way, that kind of thing, probably. And a stethoscope, which she learns to use on her little girl. And she practises her sutures. Then, using her friend’s stolen identity, she starts applying for jobs. Gets one, too: A&E doctor in an Edinburgh hospital, one that isn’t very thorough at checking references, presumably. Soon Cath is straightening out feet that are pointing the wrong way and saving victims of road traffic accidents. She keeps one of her How To books in a pocket for a sneaky peek if she needs it, plus she can always go to Doctors Google and YouTube for second opinions. What takes most people more than 10 years, Cath has achieved in a little under three months. Well, she did have a head start, being a nurse. And she was more capable and sensible than most of the doctors she worked with, both the floundering junior ones and the arrogant, complacent seniors who think they know it all.

Quite a big ask? Well, you might say so, if it didn’t happen so often in the real world. And Trust Me creator Dan Sefton knows it; he’s not just a screenwriter – he’s also a doctor working in the A&E department of Taunton hospital. Trust him.

Perhaps most surprising, given that it’s written by a real doc (unless Sefton’s a fake, of course: can someone – his hospital preferably, if they have the resources – do some checks please?), is how sympathetic a character Cath is. She is not some sick monster (I don’t think Whittaker does sick monster, does she?) playing with people’s lives. Sure, she’s committing a serious crime, and she makes a few mistakes, sticks the wrong thing in the wrong place in the heat of the moment. But on the whole she’s not doing too bad a job, hasn’t killed anyone, yet. And her motivation – wanting a bit more for her little girl – is honourable enough. God, I hope Jeremy Hunt isn’t watching; he might see sticking any old person into NHS emergency departments as a solution …

That ambiguity adds a bit of complexity and interest to Trust Me. Plus there is the crossover with the real world – NHS in crisis, job shortages, low morale, no resources, etc. Otherwise, it’s not the subtlest or most nuanced of hospital dramas; it’s straightforward and well-signposted almost to the point of clunkiness. Closer to Casualty/Holby than Jed Mercurio’s dark, masterly Bodies.

As for Whittaker, there aren’t many clues here as to what kind of Doctor she will make. She is warm and watchable, as ever, but this part doesn’t give her the opportunity to show the wit that I hope she will bring to the Tardis, and which that role requires.

Maybe she is a fake Doctor, too. She was just at Peter Capaldi’s leaving party (even though he hasn’t left yet), came across his sonic screwdriver; now she has got a few months to bone up on time travel.