British and Irish leaders eased fears over the near collapse in Brexit talks on Thursday after they declared both saw a "path" to a deal before the October 31 deadline for exit from the EU.

After a three-hour meeting near the northern city of Liverpool, Boris Johnson and Leo Varadkar issued a joint statement that indicated negotiations could be revived after coming to a standstill earlier in the week.

Sterling staged a modest rally rising half a percent to $1.2281 follow the statement.

It revealed there had been a detailed and constructive discussion at a hotel near the city.

"Both continue to believe that a deal is in everybody’s interest. They agreed that they could see a pathway to a possible deal," it said, adding the focus would shift to the Task Force 50 European negotiating team and its British interlocuters. "Following their discussions the Taoiseach will consult with the Taskforce 50 and the Brexit Secretary Stephen Barclay will meet Michel Barnier tomorrow morning."

Mr Varadkar added the process was at a very sensitive stage and there remained issues to be resolved. "I had a very good meeting, very positive and very promising," he said.

There are two outstanding impediments to Britain's hopes to renegotiate the Withdrawal Agreement that its parliament has rejected three times. The first is how to keep Northern Ireland in a seamless trading relationship with the Republic of Ireland. The EU has said the British run territory must remain in a customs union while London wants a free trade arrangement.

The second is a means of ensure Northern Ireland can approve any special arrangements at the ballot box.

"Their discussion concentrated on the challenges of customs and consent," the statement added. "They agreed to reflect further on their discussions and that officials would continue to engage intensively on them."

The atmosphere surrounding the negotiations was soured as the two sides blamed each other for their failure to make progress.

Thus the joint statement from Johnson and Varadkar marked a positive shift in tone. But it also highlighted the difficulties the negotiators have faced, notably on agreeing arrangements for customs checks on goods crossing the Irish border and how the region’s community could give its consent to these plans.

As one of the smallest states in the EU and the only country that shares a land border with the UK, Ireland has sought to ensure that negotiations on exit are routed through Brussels.

The bilateral talks with Mr Johnson were described by Irish officials as "about the process for securing agreement for a Brexit deal” and not, Irish sources pointed out, about actually securing an agreement on the substance on how the UK leaves the EU." according to the Dublin media.

After Mr Barnier declared on Wednesday that the British proposals were "not acceptable", Mr Johnson was under pressure to provide a shift in Britain's position over the customs arrangements across Ireland following Brexit.

French President Emmanuel Macron voiced frustration on Thursday, saying: "Brexit is a British domestic crisis, not a European one."

He said what was important now was to finalise negotiations and see if there was "something that I hope could fly".

"At the very end this is a British responsibility" on whether it leaves the EU with or without a deal or even cancels the Brexit process outright, he added.

Meanwhile Britain's security minister Brandon Lewis warned EU citizens they must apply for settled status or risk being expelled from the UK if they failed to use a new scheme to establish residency. Asked about figures showing only a third of Germans living in Britain under EU freedom of movement regulations had so far applied to be registered and Lewis said "theoretically, yes,” when asked if they could be removed from the country if there’s a no-deal split.