Theresa May is set to become leader of the Conservative Party and the next British Prime Minister on Wednesday evening after her leadership rival Andrea Leadsom pulled out of the race yesterday. May confirmed that the UK would continue the process of leaving the EU, despite suggestions from some parties that the referendum result be ignored.

May’s predecessor David Cameron will travel to Buckingham Palace on Wednesday morning to tender his resignation to the Queen before May takes up residence in No. 10 Downing Street later in the evening. Cameron announced that he intended to resign following the Brexit vote, but he had said he would stay on as Prime Minister until October when it was believed a new leader would be appointed. Leadsom’s decision to pull out of the contest, however, eliminated the need for a nine-week campaign before party members vote and May has since been confirmed as Prime Minister-elect.

Taoiseach (Irish Prime Minister) Enda Kenny is set to seek an early meeting with May as she begins the task of overseeing the UK’s departure from the EU. Kenny enjoyed a good relationship with Cameron. Kenny is believed to have felt that May was the best candidate to take over as Prime Minister despite concerns Irish government misgivings over May's commitment – expressed earlier this year – to take Britain out of the European Convention on Human Rights. The Irish government warned that doing so would be a breach of the 1998 Belfast Agreement (Good Friday Agreement) and threaten the peace in Northern Ireland. May later changed her position.

Irish government officials told the Irish Times that May has previously been involved in Irish affairs during her seven-year stint as Home Secretary, a role considered one of the toughest in the British cabinet.

“She managed to survive in the Home Office for seven years. So we would obviously respect that,” one official said.

Irish Minister for Justice Frances Fitzgerald also commented on her previous co-operation with May.

“She’s very easy to work with, very pragmatic, very clear,” she said.

“We worked closely together on justice and home affairs issues, and she is familiar with Northern Ireland issues.”

Northern Ireland First Minister Arlene Foster said: “Theresa May has a positive history of working with the Northern Ireland administration across a range of Justice issues,” Foster said.

“The withdrawal of Andrea Leadsom means our new Prime Minister will be in place within a much shorter time frame than previously thought which helps reduce some of the political uncertainty.”

Meet #TheresaMay - Britain's next Prime Minister ...

— ITV News (@itvnews) July 11, 2016

Foster, who campaigned to leave the EU, also welcomed the new Prime Minister’s commitment to upholding the Brexit referendum result, despite the fact that May herself campaigned to remain.

“I welcome the fact that Mrs May has indicated that the UK will exit the European Union in keeping with the result of the referendum,” said the First Minister.

“It is important that she can commence work on planning the UK exit and the new arrangements to be negotiated.”

May rejected proposals to ignore the referendum result at her campaign launch yesterday morning, confirming that she would oversee the country's withdrawal while Prime Minister.

“Brexit means Brexit and we're going to make a success of it,” May said.

"There will be no attempts to remain inside the EU, there will be no attempts to rejoin it by the back door.

"As prime minister, I will make sure we leave the European Union."

Her comments came as the finance ministers from the three devolved administrations of the UK met to discuss the impact of Brexit. Scottish Cabinet Secretary for Finance Derek Mackay met with his Northern Irish and Welsh counterparts Máirtín Ó Muilleoir and Mark Drakeford to discuss public finances in the future.

“The impact of the EU referendum has created uncertainty and challenges for us all across these islands,” Ó Muilleoir stated.

"It is therefore critically important that the three devolved administrations work together closely on financial areas of common interest."

“It is vitally important that she hears Northern Ireland’s voice loud and clear and that means bringing an end to the period of drift which seems to have engulfed the Northern Ireland Executive," stated Ulster Unionist leader Mike Nesbitt.

During the referendum campaign May stated that it was “inconceivable” that Northern Ireland would not see changes to the border with the Republic when it leaves the EU.

Speaking in Northern Ireland just days before the vote, the Prime Minister-elect stated that tariffs would have to be put in place.

Read more: Irish passport forms sell for $130 on eBay due to Brexit panic

Chancellor George Osborne says #TheresaMay has "got the steel and determination to do the job" and the economy needs certainty

— Sky News Newsdesk (@SkyNewsBreak) July 11, 2016

We'd be fools to think #TheresaMay as PM will make the Tories a more compassionate gov't b/c as Home Secretary she was one cruel minister.

— Harry Leslie Smith (@Harryslaststand) July 11, 2016

Need I say anymore? #TheresaMay

— Monica Craven (@monica_craven) July 11, 2016

Congrats to #TheresaMay was backing her for PM great result & our 2nd female PM! ��������

— Luisa Zissman (@TheLuluLife) July 11, 2016