Leveson Sketch: If there’s one thing worse than MPs tearing each other to pieces, it’s when they agree

So was it D-Day as the The Sun called it on its Churchillian front page today? Or Munich, as it was no doubt tempted to call it tomorrow?

Either way the early-morning deal struck between the main parties was the signal for an orgy of mutual congratulation across much of the Commons today.

Because MPs are so used to slagging each other off, they find it almost impossible to do agreement in terms other than cloying.

The Liberal Democrat Simon Hughes paid tribute to so many people you thought he was never going to stop: Lord Justice Leveson, Cameron, Clegg, Miliband, Harriet Harman, their staff, their special advisers, the parliamentary clerks and others “who had worked beyond the call of duty” and shown “an absolute will to solve the problem in time”.

The problem was that the agreement was so fresh – and fragile – that you worried that it could easily unravel in the face of all this flattery and consensus.

Hughes himself got so carried away that he drew sardonic laughter when he pointed out that even MPs had now accepted an element of independent regulation. This did not go down well.

A horrified Conservative, Peter Bone, suggested that if he was suggesting a body modelled on the hated Ipsa, set up in the wake of the MPs expenses scandal and “which had reduced the effectiveness” of our elected representatives, then “we have something to worry about”.

Heavens no. “That is not the model,” Hughes assured him.

Similarly, it wasn’t clear that Cameron particularly enjoyed the gratitude so courteously visited on him by Labour MPs, including Ed Miliband, for, as they saw it, his agreeing to a large part of what they had pressed for over the weekend. Any more than he must have enjoyed Nick Clegg agreeing with Miliband that “of course” the deal involved “statutory underpinning” of the Royal Charter, when the Government had earlier been spinning just the opposite.

Gamely, Cameron was obliged to admit the obvious – in answer to a question from the Labour MP Ian Lucas – that the changes would indeed require two important but “relatively small” legislative changes.

He was helped, oddly, by Labour’ elder statesman Gerald Kaufman, who in backing the deal, issued such a paean of praise for a free press that he said that he would even prefer a “corrupt” fourth estate to one that was regulated by the state.

This at least helped – for the moment – to knock on the head the hyperbole that the post-Leveson changes would consign the British press to conditions no better than existed in the Soviet Union at the height of Stalin’s power.

Even so, Cameron – sensibly, if only implicitly – nodded to The Sun, by using the quote it had emblazoned all over its front page from Winston Churchill, that a “free press is the unsleeping guardian of every other right that free men prize”.

He was treading a tightrope, not least because of angst among some of his own MPs.

And you didn’t have to agree with a highly critical Peter Lilley or the independent-minded Sarah Wollaston who said that she saw the “white flag” rather than “white smoke” emerging from the deal to find it a relief from the self-reinforcing mood of the day.

That said, the consensus mattered, since what became clear yesterday is that if the “closed” sign really was going to be put up outside the “last chance saloon”, as Gerald Kaufman insisted it was, you almost certainly needed it in the face of sections of the press implacably opposed to such changes.

It’s called huddling together for warmth.