SO the lady is for turning. And so too is the gentleman for that matter.

After a marathon Cabinet meeting, Theresa decided to offer Jeremy the chance to thrash out a May-Corbyn deal to crack the iron-clad nut that is Brexit.

On Monday night, it was interesting to see how the Labour leadership moved to back the Norway-style option, meaning a manifesto pledge to end free movement went out of the window.

Last night, the Tory leadership signalled it was willing to ditch its red lines on not countenancing continued membership of the single market and the customs union. Which were, of course, in the 2017 Conservative manifesto.

This is the logical conclusion of what the PM told the nation from Downing St last night.

If things came down to a parliamentary penalty shoot-out between Mrs May’s deal and another option – probably a customs union given this was the alternative that came the closest to winning a majority – then, if this other proposal were to pass, the PM would have to go to Brussels to make the case for it.

“Crucially, the Government stands ready to abide by the decision of the House,” declared Mrs May to the TV cameras.

Equally, Labour would have to sign the agreement in political blood; so that if the PM’s plan won the vote, Mr Corbyn and his comrades would have to support it.

But, of course, firstly the two leaders will meet in Downing St for beer and sandwiches or more likely diet coke and vol-au-vents to try to avoid a run-off and get both sides behind a “single unified position”.

No 10 insisted Mrs May would approach the talks in a “constructive” way while Mr Corbyn made clear he would “not set any limits”.

But the very thought of an attempt to mingle the thoughts of Maggie May and Comrade Corbyn has sent the Brexiteers into eye-rolling disdain, summed up nicely by the Old Etonian Chairman of the European Research Group. “Getting the support of a known Marxist is not likely to instil confidence in Conservatives," declared Jacob Rees-Mogg.

The Tory turmoil has already seen Labour push its nose five points ahead of its rival in the latest poll.

The reality is, as Chief Whip Julian Smith conceded in the BBC documentary, a minority government faced with the Brexit mountain was never going to scale it without help from the other side. So the centre of political gravity at Westminster always meant Mrs May was destined to accede to a softer Brexit if a no-deal was off the table.

Compromise, someone somewhere once said, was the art of politics. We are about to find out how artful Mrs May and Mr Corbyn can be.

Asked what would happen if a run-off did not produce a majority for any option, a No 10 source said softly: “We’re very much hoping it does.”