She then has some breathing space of up to seven ‘sitting days’ of the Commons (January 30), before MPs vote again on any new deal. Sources suggest the fresh vote would take place later next week.

May desperately needs something new to persuade both Tory and DUP MPs that the UK won’t be locked indefinitely into the controversial Northern Ireland backstop, the link to EU trade regulations aimed at keeping the border with Ireland open.

That “something” may be a new UK-EU joint legislative document that clarifies in law that Britain will not be tied to Brussels rules without end. The EU has made clear it won’t renegotiate the withdrawal agreement for Brexit, but it might grant this concession to avoid a no-deal.

However, with a massive number of her own MPs against her, May’s ‘Plan B’ can’t really be ‘Plan A-plus’. She has a nightmare balancing act now: offer Labour MPs too much and she risks further bleeding Tory support; offer Tory MPs too much and the EU will never accept it.

She’s a zombie PM in a zombie Parliament, and may get only one more time to resurrect her deal from the dead.

Will MPs back a softer Brexit?
A so-called ‘Norway-style’ Brexit is being pushed by some Labour and Tory backbenchers. It aims to keep the UK in the EU single market, ensuring free trade to continue on services, which makes up 80% of the UK economy.

The plan also aims to achieve a customs union with the EU, a key element that would remove the problem of the Northern Irish border.

For some MPs there are major downsides, not least that the single market would mean no new curbs on EU migration, something many Leave voters have demanded. A customs union would also mean the UK couldn’t strike its own free trade deals independently of Brussels.

Both of these are ‘red lines’ for the PM and many Tory MPs who think it would mean ‘Brexit in name only’ (also known as ‘Brino’). But if May’s own deal is rejected repeatedly she may have no choice.

Straight after the defeat, a No.10 spokesman said May’s talks with MPs would take place on the ‘basis’ of her current deal, with the ‘principles’ being that the UK took control of its ‘money, borders and laws’ and retained an ‘independent trade policy’.

Each of those ‘red line’ principles may have to be erased. An independent trade policy is impossible if May supports a customs union. Control of borders is very difficult if she backs a single market.

A ‘Norway-style’ Brexit would need more negotiation with Brussels and probably therefore an extension to Article 50. Some argue, however, that because the plan makes the Northern Ireland backstop irrelevant, May’s withdrawal agreement could pass and the ‘political declaration’ tweaked instead.

The main attraction of ‘Norway Plus’ for Labour MPs, possibly including Jeremy Corbyn, is that it is consistent with his pledge at the last election to uphold the 2016 referendum result. Tories would have to swallow a lot, however, to accept it.

Will the Commons get to choose which ‘Plan B’ it wants?
The real action on Brexit talks between May and other parties starts next week. MPs held off proposing their alternatives today because they wanted a clear signal that May’s deal was dead first.

It is now up to them to work out which ‘Plan B’ can get a majority, with detailed amendments to the government’s next motion. But tactics will come into play too.

Supporters of the rival plans for a ‘Norway-style’ Brexit and a second referendum want their solution to be the last one standing after all the other options have failed.

On this, as on many other matters of procedure, the Speaker of the Commons suddenly assumes even more importance than usual.

Thanks to a hung parliament tying the government’s hands and to his own decision to tear up previous conventions, John Bercow is now a very important figure. He may, for example, refuse to allow May to keep bringing back her deal several times.

There is one other option: the PM could proactively agree to demands from some of her Cabinet ministers to hold a series of ‘indicative’ votes on each of the options. But No.10 sources suggest that’s unlikely.

Are we heading for a no-deal Brexit?
Under the EU Withdrawal Act 2018, the default position is that the UK will leave the EU on March 29, 2019 – with or without any agreement.

Many Tory Brexiteers have hoped that they can thus “run down the clock” while the Commons squabbles over Brexit, and just wait for exit day to arrive.

Theresa May’s language has changed dramatically on this in the past two years. In January 2017, she uttered the infamous line that “no deal is better than a bad deal”. Having lost the last election, she’s been forced to now effectively threaten Tory MPs that “my bad deal is better than no Brexit at all”.

Some Cabinet ministers say that May has also changed tack after reading detailed forecasts from civil servants setting out the full “disaster” for trade, and, crucially, security policy if we quit without a deal.

Labour has long argued no-deal is a negotiating “bluff”, and despite billions being spent on emergency contingency plans, it looks very much like a bluff now.

Yet the only way to be sure to halt no-deal is if parliament gives May no choice politically, and possibly legally. That’s why Nick Boles’ new EU Withdrawal Bill is being seized on as a way through the logjam. It could ‘instruct’ May to choose whatever ‘Plan B’ the Commons agrees on.