LONDON (Reuters) - Prime Minister Theresa May must convince the European Union to curtail or even remove a key provision in Britain’s Brexit agreement if her last-ditch bid to win parliamentary support for her deal is to succeed.

FILE PHOTO: Britain's Prime Minister Theresa May leaves Downing Street in London, Britain, January 21, 2019. REUTERS/Toby Melville/File Photo

May said on Monday she would seek further concessions from the EU to break a deadlock in parliament, repeating the tactic she tried last year - without success - to focus on winning over her own party rather than courting opposition MPs.

Some in her Conservative Party share the main opposition Labour Party’s description of her strategy as “groundhog day” and are unmoved by threats that parliament could seize control of the process and delay or even block Brexit.

But others say they could be won over if she manages to secure concessions on the so-called Northern Irish backstop, an insurance policy to keep the border open between the British province and Ireland if a future trade deal falls short.

With only a matter of weeks before Britain is due to leave on March 29, the problem is that Brussels, so far, says the backstop is non-negotiable, and the arithmetic in London’s parliament is as complicated as ever.

“The deal is more capable of a resurrection than it ever has been, but it’s up to the EU. The EU has to play ball,” said David Jones, a Brexit-supporting former minister.

“If they were to remove the backstop then some Brexiteers might peel off and support the deal. A time limit might also be ok,” he said.

Changes to the backstop could also be enough to win the support of the Northern Irish Democratic Unionist Party (DUP), whose 10 MPs prop up May’s minority government but have so far voted against her deal.

The future of Britain’s 2016 vote to leave the EU has never been so uncertain and May has been accused of “running down the clock” to pressure her Conservatives and DUP allies to back her deal.

More than 430 MPs voted against May’s deal last week, the biggest defeat of a government in modern history despite her efforts to ease the concerns of many in her party over the divorce deal. She needs more than 100 of those to change sides.

FOCUS MINDS

But as the departure date gets closer, minds may become more focussed, the theory goes, by the threat of leaving without a deal or by the risk of some pro-EU MPs trying to seize control of Brexit to usher in a closer relationship after March or even to stop Britain from exiting.

The hardline Brexit supporters are unlikely to shift, but Mark Harper, a Conservative lawmaker who voted against May’s deal, said he believed if the prime minister could change the withdrawal agreement then “my judgement is that most Conservatives who voted against the deal last week would be prepared to support a revised deal” notwithstanding their other concerns.

May has said she is listening to MPs’ concerns about her deal, which envisages close economic ties with the EU after Brexit, and signalled this week that she would renew efforts to win over her party and the DUP.

But May faces a struggle to get the EU to shift - accommodating suggestions from Poland were shot down by Ireland this week as being out of step with Brussels’ stance.

EU Economic Affairs Commissioner Pierre Moscovici said in Davos on Wednesday the risk of a no-deal Brexit had increased and it was up to the British to tell the EU how they proposed to break the impasse.

The prime minister knows she must offer some change to the overall package of the withdrawal agreement and future partnership to get her agreement through parliament.

Late last year, Britain tried to get the EU to agree to setting a start date for the future trade relationship after Brexit, rather than trying to agree an end date for the Irish border guarantee. But negotiators were rebuffed.

For now, many in parliament are waiting to see who moves first. May is due to speak in parliament on Jan. 29.