How big does a bath need to be for ‘sex frolicking’ to be a possibility? That’s not, if you’d asked anyone six months ago, the question on which the reputational future of the monarchy might be in part held to depend – and yet here we are. Outriders for the Duke of York – who still seems dementedly convinced there exists a path to clearing his name, and that pursuing it will in no way make things worse – have released a trial balloon for his latest line of attack against Virginia Roberts Guiffre’s claims that he abused her while she was a teenage sex-slave of Jeffrey Epstein.

The photograph made the front page of the Daily Telegraph, no less. It showed two people, described in the accompanying story as ‘acquaintances’ of Ghislaine Maxwell, sitting facing each-other, fully clothed, in the bathtub of Maxwell’s old home. Each of these people had their faces obscured by a sheet of A4 paper tied round their heads with a bit of string, one of them bearing an image of Prince Andrew’s face; the other of a teenage Virginia Roberts Guiffre.

One of the reasons this story was at once funny, poignant and insane is that the bathtub really did look like rather a big one

An accidental David Lynch vibe, there, and one nobody’s nightmares will thank them for. The headline read: ‘The photo that ‘clears Duke’ over bath sex.’ Ghislaine Maxwell’s older brother Ian explained to the newspaper: ‘I am releasing my photographs now because the truth needs to come out. They show conclusively that the bath is too small for any sort of sex frolicking…’

One of the many reasons that this story was at once funny, poignant and extremely insane is that the bathtub in the picture really did look like rather a big one. The idea, clearly, was that everyone who saw the picture would chorus as one: ‘OBVIOUSLY there’s no chance of nookie in a tub that size. The story simply doesn’t hold up.’ Instead, most of us will, I think, have seen the man in the Prince Andrew mask comfortably recumbent and his opposite number, at the tap end, sitting up straighter but with a fair bit of room for manoeuvre, and thought: ‘Yup, you totally could.’

And at once, we will have started speculating on the different forms of frolicking that might be possible if you don’t mind the odd bumped elbow and a soggy bathmat. Anyone who happened to have a couple of lay figures to hand, a smutty imagination and an idle ten minutes will have been able to compile a pretty creditable list. In the section marked ‘Easy peasy’ on that list would be the frolic whose possibility the photograph is specifically designed to rebut, viz ‘he started licking my toes, between my toes, the arches of my feet’.

Even from my limited, now rather long-ago experience in the field of ‘sex frolicking’, I know that you can absolutely pursue the hobby in an ordinary sized bathtub. People, with enough determination, have sex-frolicked in all sorts of confined spaces. Boris Becker managed it in a broom cupboard in Nobu. James Bond once did it in a space capsule. There was sex-frolicking, if his songs to be trusted as documentary evidence, in the cramped front seat of every car Meat Loaf ever owned.

So, as I say, this photograph doesn’t disprove anything like what it is intended to disprove. But it is probative in an entirely different way. It shows, I’m afraid, that Prince Andrew (and/or his idiotic enablers) is as near as makes no difference to going clean off his rocker. Anyone with a remotely well-calibrated understanding of the world would be able to see that his reputation is shot, and that having friends of Ghislaine Maxwell (another person who, let us say, is ‘reputationally compromised’) planting stunt stories in the press isn’t going to unshoot it.

He would see that even if, let us say for the sake of argument, Miss Roberts Guiffre made the whole thing up, his response to her accusations has been such as would incline most onlookers to end up believing her rather than otherwise. He claimed never to have met her. A friend of the Duke claimed that a photograph showing him with his arm around her was photoshopped because he has fatter fingers than that. There was all that mad nonsense about a medical condition making it impossible to sweat and the Woking branch of Pizza Express. There were the tawdry briefings from his legal team that she was a slutty gold-digger. There was the Keystone-Cops-style dodging of process servers and haggling over jurisdictions. And finally, though declining to admit any wrongdoing, he paid her off in a confidential settlement.

He would have to be stark mad to imagine that, at this stage, there’s even the faintest hope she’ll turn round and say: ‘You know what, fair play to you – I got the wrong man. I withdraw the whole thing. Here’s your money back with interest and a full public apology.’ It is obvious, nevertheless, that he clings to such a hope; that it has been nourished by Ms Roberts-Guiffre withdrawing her similar accusations against the lawyer Alan Dershowitz with the admission that she may have identified him wrongly; and that whoever currently serves him in the role of ‘friend and confidant’ is wickedly encouraging him in it. The idea of ‘overturning the settlement’ still dances ahead of him like an ignis fatuus – and we know where they lead travellers in folklore.

What’s to be gained? Nothing, surely, for the disgraced Duke. Even if the settlement is somehow overturned on a technicality – they’re still wibbling on about jurisdictions – there’s not a hope in hell that will translate to the return to public life and royal privilege he craves. His older brother, like his late mother, has so far stopped short of cutting him off altogether. The King is reported privately to have given Andrew financial support, and he has not banned him altogether from family events. In doing so, he has put fraternal solidarity ahead of reputational contagion. Quite how long his patience will last if more of the splashes ahead of his coronation are from ‘sex frolicking’ in Ghislaine Maxwell’s bathtub is anyone’s guess.