In 2007, the papers were full of news of John Darwin, who turned up more than five years after he was declared dead in a canoeing accident so his wife Anne could claim the life insurance payout. He was living next door to the family home in County Durham– an inherently fascinating situation, as demonstrated by the acres of news coverage at the time.

This is the inspiration for Can You Keep A Secret?, which certainly has its share of intrigue and peril – as within minutes of the first episode starting, Debbie Fendon (Dawn French) confesses to her adult son Harry (Craig Roberts) that his father William (Mark Heap) isn’t actually dead, as she’d led everyone to believe.

We get the story of why this happened, amusingly told with the present-day family watching on like Dickens’ Christmas ghosts, as a GP with a fear of diseases signs off the death certificate and a rather convenient mix-up at the funeral parlour allows the family to bury a random body. The drama  obviously comes from whether they’ll get away with their £250,000 fraud, especially as Harry’s wife Neha (Mandip Gill) is a police officer.

As you might hope, the performances are great. Heap does what he does best, being an idiosyncratic, slightly isolated man away in his odd world. The joke is that  William complains about going  into hiding, but he never goes out anyway. ‘The wonderful thing about you is that you might as well have been dead for the past 30 years,’ Debbie tells him, more lovingly than it sounds.

French partly plays to type as the woman who holds things together and gets things done, though with less empathy than Rev Geraldine Grainger had. She exhibits a darker controlling streak and has no truck with her son being on anti-depressants – they’re for other people. Perhaps she needs to be more  controlling, however, as it soon emerges William has Parkinson’s disease - and the fact their insurance never paid out when he was diagnosed justifies the crime, at least in her head.

Writer Simon Mayhew-Archer’s father Paul – who co-wrote the Vicar of Dibley with Richard Curtis – also has the condition, which adds an element of veracity to the family’s desperation, however silly things get.

William’s peculiar behaviour is the richest strand of jokes, though his incontinence lands oddly. It seems played for laughs, but the show is otherwise relatively compassionate to the fraudster family, and your sympathies do lie with him. Mayhew-Archer certainly likes below-the-belt humour and there’s a running gag about a local weirdo’s penchant for petrol pumps, which works despite – or because of – its unsophistication.

Judging from the first episode, the comedy is uneven but generally seems pitched at the level of Am I Being Unreasonable? or Man On The Inside, where you don’t really laugh much but are compelled by the intrigue plus very watchable performances from seasoned pros who make you root for them. 

• Can You Keep A Secret? airs on BBC One at 9.30pm tonight, and all episodes are on iPlayer now.