Theresa May’s tough EU summit has seen her return from Brussels without the legal alterations to the Brexit deal demanded by MPs opposed to the agreement.

As the Prime Minister considers what her next move might be, here is a look at some of the options open to her.

– More talks

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German Chancellor Angela Merkel Theresa May during a round table meeting at the EU summit (Alastair Grant/AP)

Despite fellow EU leaders rejecting her appeal for changes to the Withdrawal Agreement, the Brexit legal text, Mrs May said talks would continue over ways to win over enough MPs to pass the deal.

The EU27 have said they will do their utmost so that the backstop – intended to ensure there is no return to a hard border between Northern Ireland and the Republic – will not be needed.

While the leaders may give more (non-binding) political assurances, they have insisted they can not re-open the terms of the agreement.

With the likelihood of legal changes being made diminishing, members of Mrs May’s own Cabinet have reportedly been openly discussing alternatives.

– Cross-party alliance

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Jeremy Corbyn speaks following Theresa May’s statement in the Commons, where she delayed the “meaningful vote” on her Brexit deal (House of Commons/PA)

Facing the prospect that she will not have the support of enough of her own MPs and the DUP to pass the withdrawal agreement in its current form, Mrs May could appeal to MPs across the Commons for support.

Even though they are from rival political tribes, some opposition MPs may feel that backing the PM’s deal is a pragmatic way forward to reduce the likelihood of a no-deal Brexit, a second referendum or no Brexit at all.

Several senior Tories have encouraged the PM to open discussions with MPs outside her party, while her former policy chief, George Freeman, also encouraged her to “pivot to a cross-party Brexit Plan B”.

With Jeremy Corbyn describing her deal as “dead in the water”, Mrs May would have to hope some backbench Labour MPs are sympathetic to her cause.

– Norway for now

A softer route to EU withdrawal, which was proposed by backbencher Nick Boles and backed by some Labour MPs, would see the UK take on temporary membership of the European Economic Area (EEA) and European Free Trade Association (Efta) alongside countries like Norway and Iceland while a future trade deal is negotiated.

Efta membership would allow the UK to remain within a common market area with the EU and continue existing customs arrangements, while pulling out of common agricultural and fishing policies.

It would solve the border problem with Ireland, but critics say it would mean accepting freedom of movement for EU citizens.

– No deal

The staunchest Brexiteers, like Jacob Rees-Mogg and John Redwood, say Britain has nothing to fear from EU withdrawal without a deal.

This would involve the UK falling back on World Trade Organisation rules which provide baseline requirements for tariff and customs arrangements between countries outside trading blocs like the EU.

Critics say this would result in high tariffs on many goods and exclusion from existing Europe-wide systems in areas such as aviation, food safety and credit card payments, with a damaging impact on the UK economy.

But advocates of no deal insist the UK could offer low- or zero-tariff trade to partners and benefit from swift free-trade agreements around the world while saving the £39 billion “divorce” payment to the EU.

– Second referendum

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Members of the public march in support of the People’s Vote campaign in Liverpool (Peter Byrne/PA)

Supporters of the People’s Vote campaign want a referendum on any withdrawal deal – or no deal – with the option of remaining in the EU on the ballot paper.

They argue that voters in the 2016 referendum which delivered a 52%-48% majority for Leave did not have the full information about what Brexit would involve, and should have a chance to make a decision based on a clearer understanding of the terms on offer.

EU leaders have indicated they would be happy to accept Britain staying on as a member, and campaigners hope Brussels would be willing to put the Brexit process on hold to give time for a public vote to be held, probably in late spring.

Opponents of a second referendum warn that faith in democracy will be undermined if the Government does not deliver on the outcome of what was the UK’s largest-ever ballot.

– Extend Article 50

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Theresa May signs the Article 50 letter (Christopher Furlong/PA)

The letter which triggered the process for Britain leaving the EU was delivered on March 29 2017, starting a two-year process of departure.

Mrs May alluded to the extension of Article 50 when faced with a vote of no confidence, saying any successor’s first job would be to delay Brexit, but any agreement to lengthen the process would have to be agreed unanimously.

Equally, the European Court of Justice ruled this week that Britain could rescind Article 50 if it wanted, however it is unclear whether Mrs May would receive political backing for such a move without taking the idea to the electorate.