So what next? The six options that remain on the table

SHE may have survived the no-confidence vote, but the scale of opposition to Theresa May’s Brexit deal was laid bare, with 117 Tory MPS voting against her and the Democratic Unionist Party still implacably opposed.

With the parliamentary arithmetic pointing to deadlock and stalemate, Mrs May may need to take radical steps in order to advance Brexit. Here are the options that confront her:

The EU bends on the backstop

The Irish backstop remains the biggest obstacle to Parliament backing Mrs May’s deal, with Brexiteer MPS adamant that they will not support any arrangement that does not contain some kind of exit clause to avoid the UK becoming trapped indefinitely in a customs union.

The EU is equally adamant that it will not drop the backstop, and that it must remain in place until alternative arrangements are in place – whether a permanent customs union, a customs border in the Irish Sea or some form of technological fix.

Mrs May appears to have accepted that the terms of the divorce deal cannot be renegotiated, so is instead trying to get a legally binding promise from the EU that it will try its best to leave the backstop within a year, if it ever kicks in.

If she gets this extra reassurance, she can take it to Parliament and hope that, as no deal looms, it will persuade doubters to back her deal.

Extend or rescind Article 50

If her deal still looks destined to fail, the Prime Minister could ask the EU for an extension of Article 50, the two-year period set out for the divorce negotiations in the EU treaties.

The EU is potentially amenable to this, but only in order to create the time and space for something specific – like a general election, a second referendum or to finish the legislative process to enact an agreed deal. An agreement to extend must be unanimous.

Mrs May could also unilaterally revoke Article 50 entirely following a recent European court judgment, but in practice she is likely to need a second referendum to get political assent for this move.

Slide to single market and customs union (Norway plus)

Another alternative would be to shift radically towards a super-soft Brexit in which the UK agreed to follow EU single market rules and remain in a customs union with the EU.

This might persuade Labour to back the deal,but at the cost of splitting her own party.

Such a deal would obviate much of the Irish backstop problem, come with onerous strings attached from the European Union side and require the UK to continue to accept the free movement of people.

Accept no-deal

If Parliament rejects her deal, Mrs May could try to run down the clock, letting Article 50 expire and allowing the UK to default into no-deal, and accept the serious disruption that would come from an abrupt shift on to World Trade Organisation terms.

There has been talk of a managed no deal, but the EU is clear that this would be temporary and still highly disruptive, and in the end the UK would have to return to the negotiating table – where the same set of problems would present themselves.

It also appears that the one thing for which there is a parliamentary majority is blocking a no-deal, which would require centrist Labour and Tory factions to combine to thwart a crash-out.

Call a general election

In a bid to change the arithmetic, Mrs May could call a general election.

She would need a two-thirds majority of the House, but with Jeremy Corbyn desperate to go to the polls, that would not be a problem.

However, with the Tory back benches in open mutiny and private polls showing the Conservative Party trailing in key northern constituencies, it seems highly unlikely that the backbench 1922 Committee would give its consent.

Agree to a second referendum

Lastly, faced with a total impasse, the Prime Minister could agree to a second referendum, although there are competing visions of what questions would be asked.

Would it be a rerun of 2016’s Leaverremain poll; a three-question poll including Mrs May’s deal or a two-round contest taking both of these in turn?

Whatever the question, current polling gives no clear idea which way the vote would go, but if the parliamentary and constitutional deadlock is complete, it may be the only way to move forward.