British Prime Minister Theresa May has thrown her weight behind a parliamentary move to win her more Brexit negotiating power, by rallying MPs behind an alternative to the backstop.

Conservative chairman Brandon Lewis announced that Tory MPs will be whipped to support an amendment tabled by senior backbencher Graham Brady in a series of votes on Tuesday evening.

Tory backbenchers Andrew Murrison and John Baron withdrew their rival amendments, which would have required the scrapping or time-limiting of the backstop, which is designed to avoid the need for a hard border in Ireland following Brexit.

But the dramatic move was far from guaranteed to deliver a majority for the plan, after it failed to win the support of the influential European Research Group of Conservative eurosceptics.

The amendment tabled by Mr Brady, the chair of the Tory backbench 1922 Committee, states that Parliament would be willing to support the Withdrawal Agreement reached with the EU last November, so long as the backstop is replaced with "alternative arrangements" to avoid a hard border.

Mr Brady said that he hoped that House of Commons backing would give Mrs May "enormous firepower" when she returns to Brussels to seek concessions on her Brexit deal.

However, ERG chairman Jacob Rees-Mogg said that its members, thought to number at least 60, will not support the scheme when it comes before the Commons on Tuesday.

Mrs May addressed MPs in Westminster on the eve of a day of high drama, when MPs will debate a range of rival amendments, including calls to block a no-deal departure or delay Brexit from its scheduled date of 29 March.

It comes as Tánaiste and Minister for Foreign Affairs Simon Coveney said there is no appetite across the EU to re-open the Withdrawal Agreement with Britain.

Minister Coveney also said he believes the EU would respond generously if the British government softened some of the red lines they have outlined, adding that the Withdrawal Agreement was already a balance of compromises which takes in British red lines and concerns, and also EU concerns.

He said he believed it was unreasonable to ask for the Withdrawal Agreement to be re-opened and there was no appetite across the EU to do so.

Mr Coveney suggested that the way to solve the current impasse was perhaps through the separate, future relationship declaration.

Emerging from a meeting of the ERG just moments before Mrs May’s arrival, Mr Rees-Mogg said the group would not support any amendment, but would decide on the day whether to abstain or vote against.

MPs in the ERG were concerned that the Brady amendment did not spell out what would replace the backstop and did not specify that changes to the text of the Withdrawal Agreement were required, he said.

Mr Lewis said that the Brady amendment  would "allow the Prime Minister to give a very clear message around what Parliament wants, where the party is".

Sammy Wilson of the DUP, whose ten MPs prop up the minority Conservative administration, said Mrs May should "exploit the cracks which are emerging in the illogical position of the EU and the Irish".

Insisting the UK must hold to the date of 29 March to maintain pressure on the EU and Ireland, Mr Wilson said: "Now is the time for the Government to be tough and to face down the stubbornness of Dublin and Brussels."

There was no sign in Brussels of any appetite to reopen the Withdrawal Agreement.

Chief EU negotiator Michel Barnier's deputy Sabine Weyand warned there was now a "high risk" of the UK crashing out by accident, as it was "quite a challenge" to see how a majority can be constructed at Westminster.

And European Commission vice-president Jyrki Kateinen said there was "no reason to give any concessions" to the UK and there was "not much room for manoeuvre" on the backstop.

It would be "stupid" for the EU to make concessions putting the remaining 27 members at a disadvantage simply to secure a deal, he said.

Downing Street said the PM remains committed to quitting the EU on 29 March and will take her plan back to the Commons for a second "meaningful vote" as soon as possible after Tuesday's debate.

"The Prime Minister is absolutely committed to leaving the EU with a deal, but clearly if we are to obtain parliamentary support for that deal some changes are going to have to be made," the PM's spokesman said.