Maybe it’s the hot weather, but for the past few weeks cabinet ministers have been engaged in their own private contest – I’m a Nonentity, Get Me Out of Here! – to see who can come closest to being forced to resign while still remaining in their jobs. Boris Johnson was an obvious early frontrunner until everyone remembered he had the unfair advantage of having no principles whatsoever and he was disqualified on the grounds he was a certifiable sociopath.

Since then the field has been far more open, with ministers taking it in turns to embarrass both themselves and the government, something that gets easier by the day as the prime minister’s authority flatlines. The most recent entrant – or to be more precise, re-entrant – is David Davis, a ministerial Captain Mainwaring who has never knowingly found the right end of any stick.

While most ministers have been holding fire on rubbishing Theresa May’s facilitated customs arrangement until after Chequers, the Brexit secretary has been determined to get in a pre-emptive strike. Presumably because he doesn’t want to have to flounce out after the meeting and find himself without a ministerial car and relying on one of Chris Grayling’s trains to get him home.

Captain Mainwaring hadn’t seen the FCA – he couldn’t be sure it even existed – but he was absolutely certain no one would like it and didn’t mind who knew it. If that was the best the prime minister had got, the cabinet might as well stay at home and watch the football rather than going to Chequers. He may well have been right – the mythical third way is mythical for a reason – but he couldn’t have done more to undermine the prime minister if he’d tried. She could sack him if she thought she was hard enough. It went without saying that she wasn’t.

Grayling also wakes up each morning astonished to find he still has a career. His saving grace is that no one expects any more of him than complete failure, so his hopelessness is factored into his job description. The fact that the railways have almost ground to a halt on his watch is taken as proof he has his eye firmly on the ball.

Even so, the strain is telling. Though Failing Grayling managed to avoid answering anything directly on the railways at departmental questions – he left all that to Jo Johnson, his unfortunate second-in-command – his nervous tic twitched into life every time someone mentioned the trains. If May had any compassion, Grayling would have been invalided out long ago. But it suits her to keep him lying around as he makes her look marginally less out of her depth.

Not to be outdone, Esther McVey has also upped the death-wish ante by misleading parliament on two separate occasions about the findings of a National Audit Office report on universal credit. In normal times, even to do so once would be a sackable offence, but if Brexit is to mean anything it is that the UK is a rogue state, so all the usual rules no longer apply.

On Wednesday, the work and pensions secretary had tried to pre-empt disaster by making a non-apology apology as a point of order so that no one had a chance to call her out. A day later she was brought back to the Commons by Labour’s Frank Field to face an urgent question. In his opening remarks, Field effectively said McVey had lied. Normally such language would be deemed unparliamentary, but as everyone did think McVey had lied the Speaker didn’t seek to correct the record.

“Er … I did get a letter … er … there I would like to leave this,” said McVey. You bet she would have liked to leave it there. Even a Duracell bunny runs out of power eventually, and McVey was reduced to a hesitant, incoherent wreck, albeit one who was utterly uncontrite. If she has a conscience, she keeps it well hidden.

She might have used the wrong words but that didn’t mean she was wrong. And if she had misinterpreted the bit where the NAO had said UC was a disaster then it was one of those things. Besides everyone knew the NAO was rubbish. She was sorry if people had expected her to be sorry but the bottom line was that she wasn’t sorry for anything. Sod the lot of you.

A few of the more sycophantic Tories made token offers of support, but the opposition benches piled in. At which point, McVey became delusional. She hadn’t been forced to come to the dispatch box to apologise, she insisted. She had come entirely of her own volition. The urgent question was just a coincidence.

The arrogance was as breathtaking as her lack of shame. Not that McVey cared. Her job was safe whatever she did. And that’s all that really mattered. In a post-truth world, any old lies would do.