Theresa May hopes to break the Brexit talks deadlock on Monday with a new offer on divorce settlements at a crunch meeting with EU officials, as some of her party members urge her to walk away unless there is progress.

EU officials and diplomats say they are increasingly optimistic a deal can be struck on Monday, while cautioning that things could still go wrong.

Over lunch with European Commission President Jean-Claude Juncker and European Union Brexit negotiator Michel Barnier, the British prime minister will try to persuade them to start discussions on a new trade pact and a two-year transitional deal.

The European Union has given May until Monday to put forward a more comprehensive offer on the remaining separation issues before officials recommend moving onto discussing trade and future ties.

They want a pledge that Britain will pay what it owes the bloc when leaving, protect the rights of EU citizens living in Britain and ensure there is no hard border between the north and south of Ireland.

The EU has said it will allow negotiations on the Britain's future trade relations with the EU to begin only when there has been sufficient progress on these separation issues.

Nadine Dorries, a member of Britain's ruling Conservative Party who supports Brexit, said May should tell EU officials time is running out to move talks on to the next phase.

The EU has had "enough time now to decide whether or not they are going to discuss trade with us, they need to get on with it and if they don't get on with it the closer we get to walking away with no deal", she said.

European Commission President Jean-Claude Juncker and his Brexit negotiator Michel Barnier will meet EU lawmakers early on Monday, an EU official said on Sunday.

However, EU officials and diplomats cautioned that it was still unclear that a deal would be struck with the British prime minister when she meets the EU executive.

May portrays Monday's meeting as part of preparations for an EU summit on December 15 - though the EU says Monday is the last chance for her to make offers as there will be no negotiations at the summit itself. A British spokesman said: "With plenty of discussions still to go, Monday will be an important staging post on the road to the crucial December Council."

Since the referendum in 2016, high-profile opponents of Brexit have suggested Britain could change its mind and avoid what they say will be a disaster for its economy.

Half of Britons support a second vote on whether to leave the EU, according to an opinion poll published on Sunday.

CLOCK TICKING

With the clock ticking down to the March 2019 exit date, May is under pressure to start talks on its future trade ties by the end of the year to remove the cloud of uncertainty for companies that do business in the EU.

If talks on Monday go well then EU leaders could give a green light to trade talks at their summit on December 14-15.

More than 30 pro-Brexit supporters, including members of parliament and former Conservative ministers, have signed a letter calling on May to walk away from talks unless key conditions are met.

They include an end to free movement of people from the EU into Britain and for the European Court of Justice to have no further role in British legal matters after March 2019.

With significant headway apparently made on the financial settlement and EU citizens' rights, a deal on the Irish border appears to be the main hurdle in the talks.

The almost invisible border between British-ruled Northern Ireland and the Irish Republic, a key component of the 1998 Irish peace agreement, was possible because both sides were in the EU and its single market.

Ireland has called on Britain to provide details of how it will ensure there is no "regulatory divergence" after Brexit in March 2019 that would require physical border controls.

But any solution will need the support of Northern Ireland's pro-Brexit Democratic Unionist Party, whose 10 members of parliament are propping up May's government.

The Democratic Unionist Party has said it will not support any deal that leads to Northern Ireland operating under different rules from the rest of the United Kingdom.

Irish Deputy Prime Minister Simon Coveney said on Sunday his country had "no desire" to delay the UK's Brexit talks, although not enough progress had been made so far.

An Irish government official said late on Sunday there was "still a away to go" on reaching a deal.

"The Irish government remains hopeful," the official said. "But at this stage it is very difficult to make a prediction."