LONDON (Reuters) - Over a meal of braised beef, lemon tart and fine wines, British Prime Minister Theresa May’s team tried late on Tuesday to convince some of her party’s most strident eurosceptics to back her plans to leave the European Union.

FILE PHOTO: Larry the Downing Street cat waits at the door to number 10, in central London, Britain, March 14, 2018. REUTERS/Toby Melville/File Photo

The almost two-hour dinner in the small dining room at May’s official residence in Downing Street was the second of three, part of a charm offensive by the prime minister’s team to try to quell a growing rebellion in her Conservative Party.

It is an unusual strategy, underlining the high stakes of trying to push her Brexit proposals, dubbed the Chequers plan after her country residence, through parliament despite vocal resistance from a sizeable number of her lawmakers.

Without the agreement of parliament for any deal, May could be toppled, Britain face a new election and possibly a second referendum on Brexit, the biggest shift in British foreign and trade policy in almost half a century.

But the strategy was not entirely successful. Only one of those invited said he would vote in favor of any deal based on May’s so-called Chequers plan, one source who attended the meeting said on condition of anonymity.

The others stuck to their guns, irritating May’s chief of staff by bombarding him with “pointed” questions.

“Good food, fine wines but the conversation - that wasn’t great,” the Conservative source said, describing the meeting as good-natured with no threats made to keep pro-Brexit lawmakers in line.

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“They are testing the resolve of those who will vote against Chequers and they want to whittle down the numbers.”

Another source at the dinner confirmed the account but was more positive, saying it was “a really useful exercise in terms of us hearing the government’s points about where they are in the negotiations but also for us to feed in with ideas”.

A government source said the dinners were a way “to engage with colleagues and explain our proposals”, but denied that May’s chief of staff was irritated by the questions.

REBELLION

May is struggling to win acceptance for what she calls her “business-friendly” Brexit plan, which proposes a free trade in goods by Britain and the EU adopting a common rule book, but will allow services to diverge from the bloc’s rules.

The EU has said her plan is a good starting point, but pro-Brexit campaigners fear it keeps Britain too closely tied to the bloc. They have demanded that she “chuck Chequers” and instead adopt their proposals for a Canada-style free trade agreement.

For weeks, some of her more vocal critics have been discussing possibly ousting their leader, a move that would trigger a leadership contest with only months to go before Britain leaves the EU in March next year.

Her spokesman said on Wednesday the prime minister would fight any leadership challenge, and repeated that the government was pressing on with the Chequer’s plan, a sign that May will try to force it through.

And the dinners are only part of her attempts to win her party over to the plan. Her team has invited local party leaders for discussions at Downing Street and lawmakers have sometimes been given briefings on the Brexit talks.

But one of the sources said May’s chief of staff had offered little to appease lawmakers’ concerns, arguing Chequers was the only plan on the table and suggesting that Conservative members did not support it “because of MPs like us”.

“But this will define this parliament and all of our careers,” the source said. “We’ve got to stay in government ... and she’s got to chuck Chequers.”