THE Irish Taoiseach has raised the prospect of the UK crashing out of the EU without a deal if Tory Cabinet infighting continues over the next few weeks.

Leo Varadkar made his growing concern clear before meeting the Prime Minister at an EU summit in the Bulgarian capital Sofia yesterday, as the Brexit negotiations stalled and Theresa May failed to offer any new solutions to avoid a hard border in Ireland.

Varadkar said next month’s European Council summit would be a key moment for the talks, despite attempts by the Brexit Secretary David Davis to play down suggestions of a “deadline”.

Varadkar said the EU and Dublin had “yet to see anything that remotely approaches” a way out of the current impasse.

“By June we need to see substantial progress as the Tánaiste [Varadkar’s deputy, Simon Coveney] and I have said on many occasions,” he said. “The European Council will review progress in June.

“The deadline of course for the withdrawal agreement is October, but if we are not making real and substantial progress by June then we need to seriously question whether we’re going to have a withdrawal agreement at all.”

The UK Government has been tasked by the EU to find an arrangement that will avoid the need for border checks between the Republic of Ireland and Northern Ireland, and to table a “backstop” solution involving regulatory alignment with the EU.

The EU has described two options being discussed in the UK Cabinet as not realistic and want either Northern Ireland or the whole of the UK to remain in the customs union to prevent a hard border on the island.

Cabinet Remainers want a customs partnership model which would see the UK collect EU tariffs on goods coming into the UK.

A second “maximum facilitation” or “max fac” option, favoured by the Brexiteers, would rely on using new technologies.

Varadkar said: “We need to have that backstop because that gives us the assurance that there will be no hard border on our island. So we stand by our position that there can be no withdrawal agreement without that backstop.

“If the UK wants to put forward alternatives ... we’re willing to examine that. But we need to see it written down in black and white and know that its workable and legally operable. And we’ve yet to see anything that remotely approaches that.”

Meanwhile, it emerged yesterday that ministers have agreed to tell the EU that Britain is willing to stay in the customs union after 2021 – teeing up a fresh clash with Conservative Eurosceptics.

May has previously rejected EU proposals for a backstop but according to reports her Brexit sub-committee has now agreed to stay tied to the customs union beyond the transition period at the end of 2020 – if no other solution to the Northern Ireland question can be found.

A daily newspaper yesterday reported that the plan was approved despite objections from Brexit-backing Cabinet ministers Boris Johnson and Michael Gove, who eventually relented. The plan has already drawn strong criticism from Jacob Rees-Mogg, who leads the powerful European Research Group of Eurosceptics.

He told the paper that the move risked creating a fallback option that was “more attractive than a permanent deal”.

“We have gone from a clear end point, to an extension, to a proposed further extension with no end point,” he said.

“The horizon seems to be unreachable. The bottom of the rainbow seems to be unattainable. People voted to leave, they did not vote for a perpetual purgatory.”

Speaking to the press at yesterday’s summit, May denied climbing down over membership of the customs union.

She said: “No, we are not [climbing down]. The United Kingdom will be leaving the customs union, we are leaving the European Union.

“We need to be able to have our own independent trade policy, we want as frictionless a border [as possible] between the UK and the EU so that trade can continue and we want to ensure there is no hard border between Northern Ireland and Ireland.”

The reports emerged as peers finally gave the EU Withdrawal Bill a third reading, but not before inflicting a 15th defeat on the Government. The future of the bill is now uncertain as the Government tries to estimate the risk of irreversible defeats in the Commons.