Prime Minister Boris Johnson is to travel to Luxembourg on Monday for Brexit talks with European Commission president Jean-Claude Juncker.

It will be the first time Mr Johnson has met the outgoing EU leader and chief negotiator Michel Barnier in person since taking office in July, but it is not thought to herald a breakthrough in talks on a withdrawal deal.

News of the trip emerged as Irish premier Leo Varadkar cautioned that UK proposals on border arrangements "fall far short" of what would be needed to replace the controversial "backstop".

The taoiseach told RTE radio that "the gap is very wide" between the EU and the UK in reaching a deal on Brexit.

"We have always said we would be willing to look at alternative arrangements but what we're seeing falls far short," Mr Varadkar said.

"We are exploring what is possible. The gap is very wide but we will fight for and work for a deal until the last moment, but not at any cost."

Mr Johnson's Luxembourg trip is the latest in a series of face-to-face talks with key European leaders including Angela Merkel, Emmanuel Macron, Mr Varadkar and outgoing European Council president Donald Tusk. He will also meet Luxembourg's PM Xavier Bettel, said Downing Street.

A Downing Street spokesman said that the visit was part of a continuing effort to push for a deal before the Halloween deadine by which Mr Johnson says he will take the UK out of the EU, with or without an agreement.

The spokesman said: "The prime minister is working hard to get a deal and we have been putting forward ideas but there is a long way to go."

Mr Varadkar's comments come days after talks with Mr Johnson in Dublin (REUTERS)

Mr Varadkar's comments came as DUP leader Arlene Foster poured cold water on reports that her party was about to throw the PM a lifeline by dropping its objections to a regulatory border between Northern Ireland and the rest of the UK.

Ms Foster tweeted: "UK must leave as one nation. We are keen to see a sensible deal but not one that divides the internal market of the UK."

Speaking in Rotherham at the launch of his plan to re-vitalise the Northern Powerhouse initiative, Mr Johnson said there was the "rough shape" of a deal in place.

Recent meetings with Varadkar, Merkel and Macron had made "a good deal of progress" towards an agreement.

But he made clear that if he was unable to get a new deal, he would not be deterred by "shenanigans" at Westminster from taking Britain out of the EU by the 31 October deadline.