British Prime Minister Theresa May will meet Taoiseach Leo Varadkar in Dublin tomorrow as part of her tour to secure "reassurances" from EU leaders to help get her Brexit deal through parliament.

Mrs May is visiting EU leaders this week following the deferral of the House of Commons vote on her Brexit deal.

She has visited Dutch Prime Minister Mark Rutte in The Hague, Chancellor Angela Merkel in Germany, and is due to speak to her Austrian counterpart, Sebastian Kurz, this evening.

Before she travels to meet the Taoiseach in Dublin, Mrs May will meet DUP leader Arlene Foster in London. 

The DUP leader is scheduled to meet Mrs May at 1.30pm. 

Meanwhile, the Taoiseach has told the Dáil that the Government now needs to "up the contingency planning" for a no-deal Brexit scenario.

Mr Varadkar was responding to Fianna Fáil leader Micheál Martin during Leaders' Questions in the Dáil this afternoon.

"What we have always done is based on our plans on a central case scenario which is that there would be a deal. But we have been doing contingency planning for the no deal scenario," Mr Varadkar told the Dáil.

"We now need to up the contingency planning to execution for no deal," he added.

He said this would involve accelerating the recruitment of extra customs officers, veterinary officers and health officials, and putting in place infrastructure at ports and airports.

Mr Martin warned that small and medium firms were not prepared to the level they should be.

Mr Varadkar said they had already held discussions with the European Commission on the prospect of State aid for companies who are most affected by a no-deal scenario, but he said this would not kick in unless absolutely necessary.

Mr Martin called for the briefing documents on scenarios to be published, warning that the majority of firms likely to be affected do not have plan in place.

The Taoiseach said there was no difficulty in publishing the Central Case Scenario, or the Government's plans in the event of a deal being reached.

Mr Varadkar also said the UK could remove the threat of no deal, by revoking Article 50 or extending it.

Mr Martin said that many seasoned commentators, including himself, had felt that a no-deal Brexit would not emerge, but this is no longer certain.

"The scale of the opposition to the deal yesterday was quite significant in itself. A significant period of political and economic instability lies ahead and we as a country need to be prepared for any eventuality," Mr Martin said. 

Speaking today, the Taoiseach also rejected a Sinn Féin call to plan for a border poll in the event of a no-deal Brexit.

He said demands for Irish unity at this time are destructive and disruptive.

There was a deal on the table negotiated over 15 months and the objective was to get that passed in Westminster in the next couple of weeks, he said.

Sinn Féin Leader Mary Lou McDonald had urged the Government to seek a border poll if there is a hard Brexit.

She said it was the only serious and sustainable position.

"Uniting our country would end the need for a backstop," the Sinn Féin Leader said.

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Earlier, Tánaiste and Minister for Foreign Affairs Simon Coveney said he did not believe the UK had anything to fear from the backstop as it is currently stated.

He said Mrs May was seeking further assurances about the backstop, but he did not believe she was trying to renegotiate or do away with the agreement, which was designed to avoid a return to a hard border between Northern Ireland and the Republic of Ireland.

Mr Coveney said: "Unionists need not worry that there are ulterior motives linked to the Brexit strategy of the European Union or Ireland."

He said Brexit is not about a future border poll, or any change in the constitutional arrangement of the United Kingdom.

Mr Coveney said it is about protecting the status quo, where people trade with each other and live next door to each other and where there is no physical border infrastructure between the two jurisdictions. 

Speaking on RTÉ's Morning Ireland, he said it was unrealistic to think a deal that took two years to negotiate could be renegotiated.

He said the Government was happy to offer reassurances on the backstop issue.

Former British prime minister John Major, who was attending an event Dublin, has called for the UK to revoke Article 50 with immediate effect.

"Whether you are a remainer or a leaver, no one can welcome chaos. We need to calm markets, protect economic well being of British people," said Mr Major.

"It is time to revoke Article 50 with immediate effect."

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Reporting: Edel McAllister, Mícheál Lehane, Fergal O'Brien