My old, calamity-prone friend Michael Gove in charge of our country's destiny during a nuclear attack? It's the stuff of screaming nightmares: Mr Bean carrying a tray of antique Meissen china; Katie Price gaining access to the Royal Box at Ascot.

Happily, Sky's The Wargame is but a TV show and Mr Gove will merely be role-playing a British prime minister threatened by thermo-nuclear war.

Uranium-tipped missiles have been spotted over the Urals, heading in our direction – or something like that. Sound the klaxons. Take shelter in the nearest cellar. If the prospect of deadly Kremlin warheads is not bad enough, the thought of the Gover being in charge of our national defences is even worse.

Will he order immediate retribution? Will he open the secret nuclear codes that are said to be at every PM's fingertips and tell our Trident submarines to respond in kind? More likely, knowing Michael, will he realise he left the codes in the back of his car that morning – and then sit on Downing Street's nuclear red button by mistake? A more eloquent and agreeable companion than Gove would be hard to find but he is not the most practical of men.

To make Sky's fantasy even scarier, Gove's deputy prime minister in the programme will be none other than that hapless hen Nicola Sturgeon, celebrated collector of trinketry and the woman who failed to notice that her ex-husband Peter Murrell was siphoning £400,000 out of Scots Nats funds while adorning their wee homestead with coffee machines, Le Creuset pots and pans and a £2,618 Lalique cruet. 

Scotland's former first minister claims she never spotted the ruddy great motorhome Peter parked outside his mum's suburban home. It seems a lot, therefore, to expect her to notice a few Topol-M intercontinental ballistic missiles scudding towards the coast of East Anglia.

Others taking part include former Tory MP and defence secretary Penny Mordaunt. She wore a bathing suit for her previous foray into reality TV, the diving show Splash! It may be too much to hope that she will wriggle back into her cossie for this programme but she could be useful in a combat situation. 

Just look at how she carried the Sword of State at the Coronation. And then there's Harriet Harman. It is hard to know quite why they have cast her. The brains of the operation? Labour's sometime deputy leader was never easily mistaken for a member of Mensa.

Nuclear attack, all too real a possibility given the way Vladimir Putin's grip on power is going, seems a subject of debatable taste for reality TV. Broadcasting executives will no doubt argue that there is a public-information angle. The more obvious truth may be that you never got poor in TV by being crass.

What, however, are we to make of these so-called political Illuminati agreeing to take part in such a pantomime? What's in it for them? For Sturgeon, a shot at public absolution. For Mordaunt – who would love to return to Westminster – some precious publicity. For Harman, perhaps, an excuse to tell Sir Keir Starmer that, even though he recently appointed her to a government role, she is far too busy to take his calls.

And for Michael Gove? Is he not busy enough editing The Spectator? Might he not tarnish the reputation of that publication by dabbling in such nonsense? Maybe. But for decades Michael has itched like a St Bernard with fleas to hear the words 'Yes, Prime Minister'. To be emperor of all he surveys for a few precious hours. Yes, yes, yes!

At which enthusiastic affirmative Britain's nuclear subs unleash their Tridents on Moscow, and apocalypse ensues. Oops!