The PM needs support of 320 MPs. How can she pull it off in a house of divided loyalties?

As the endlessly delayed Brexit crunch time finally draws near, many politicians’ thoughts are turning to numbers and how they relate to the success or otherwise of Theresa May’s proposal for departure.

Some of the calculations are relatively straightforward: for example, May knows she has to persuade the overwhelming majority of her 28 ministers who are in the cabinet or attend it to back the deal. It is in the Commons where things become more tricky.

How much support does May need to get her plan through parliament?

She needs the support of 320 MPs to be guaranteed a win. While the Commons has 650 MPs, 11 do not take part in voting – the Speaker, John Bercow and his three deputies; and the seven Sinn Féin MPs. That leaves 639, meaning 320 will get her over the line.

What are the state of the parties currently?

With 318 MPs – in effect 316 as Bercow and one of his deputies are Conservatives – the Tories ended up just short of a majority after the 2017 election. They have since been propped up in government by the DUP’s 10 seats.

That is about as simple as it gets, however. It remains extremely uncertain whether May can get a deal through the Commons, with a series of factors at play.

Can May rely on her Conservatives?

In brief: almost certainly not. While the bulk of her MPs would get in line and vote for a deal, she seems set to face dissent from two separate wings of the party.

Hard Brexiters in the Conservatives, notably in the European Research Group, have pledged to oppose a plan they argue would put the UK at the mercy of Brussels. How many of these would vote against the plan is extremely hard to gauge.

Even Steve Baker, the ERG vice-chair and former Brexit minister, who left government in protest at May’s plans, predicted in September that around 80 Tories would rebel, before downgrading this the following month to “at least 40”.

On the other side of the divide, a smaller but still significant number of remain-minded Tory MPs such as Dominic Grieve and Anna Soubry also dislike May’s plans, and reject what they say is a false choice of this or no deal.

They were buoyed on Friday when Jo Johnson resigned as rail minister and called for a second referendum, saying May had offered MPs the options of “vassalage and chaos”.

What about Labour?

In theory, it seems inevitable Labour will oppose May’s deal. The party has set six tests for a Brexit plan, saying it will oppose any proposal which does not meet these.

One of the tests is that a deal should bring the “exact same benefits” as currently exist under customs union and single market membership, which – despite being based on a pledge from the former Brexit secretary David Davis – is clearly impossible.

May’s lieutenants are hoping that if it came to a moment where voting down a deal would spark a near-certain no-deal Brexit or some other confusion, some Labour MPs, especially those in strongly pro-leave seats, might abstain or even back the deal.

There is also a handful of strongly pro-Brexit Labour MPs, such as Kate Hoey, who could be expected to defy the party whip.

What about the other parties?

The DUP’s support is still in the balance. While the party supports Brexit, it has also pledged to oppose any deal that treats Northern Ireland differently, for example a backstop relating just to the Irish border.

Quick guide Brexit and backstops: an explainer Show Hide A backstop is required to ensure there is no hard border in Ireland if a comprehensive free trade deal cannot be signed before the end of 2020. Theresa May has proposed to the EU that the whole of the UK would remain in the customs union after Brexit, but Brussels has said it needs more time to evaluate the proposal. As a result, the EU insists on having its own backstop - the backstop to the backstop - which would mean Northern Ireland would remain in the single market and customs union in the absence of a free trade deal, prompting fierce objections from Conservative hard Brexiters and the DUP, which props up her government. That prompted May to propose a country-wide alternative in which the whole of the UK would remain in parts of the customs union after Brexit. “The EU still requires a ‘backstop to the backstop’ – effectively an insurance policy for the insurance policy. And they want this to be the Northern Ireland-only solution that they had previously proposed,” May told MPs. Raising the stakes, the prime minister said the EU’s insistence amounted to a threat to the constitution of the UK: “We have been clear that we cannot agree to anything that threatens the integrity of our United Kingdom,” she added.

Otherwise, the rest of the MPs – 35 SNP, 12 Lib Dem, four Plaid Cymru and one Green – can be assumed to oppose May’s plans.

So will May do it?

It’s currently almost impossible to say. What seems clear is that May faces an uphill battle.