Meanwhile, her new pick for the role of the UK's ambassador to the European Union has been criticised
Theresa May's choice of a career diplomat to take over as the UK's ambassador to the European Union has been criticised by Brexit supporters.
Former ambassador to Russia Sir Tim Barrow will succeed Sir Ivan Rogers, who unexpectedly resigned on Tuesday, just weeks before formal Brexit negotiations are due to begin.
While the appointment was widely welcomed by many prominent Leave and Remain supporters, Nigel Farage was among the first to criticise the decision.
The former UKIP leader tweeted: "Good to see that the government have replaced a knighted career diplomat with... a knighted career diplomat."
UKIP said the role should have been given to a committed Brexit supporter.
Mr Farage's successor Paul Nuttall said: "I welcome the speedy appointment of Sir Tim Barrow but he has to show that he's UKRep to the EU, not EURep to the UK."
Sir Ivan sent shockwaves through the political establishment with a scathing resignation email to his staff, in which he accused Number 10 of "ill-founded arguments and muddled thinking" over leaving the EU.
Confirming his replacement, Downing Street said Sir Tim was a "seasoned and tough negotiator" who will help the Government make a success of Brexit.
He is a career diplomat who has had two previous spells working as part of the UK's Permanent Representation to the EU (UKRep), having joined the Foreign Office in 1986.
Sir Tim said: "I am honoured to be appointed as the UK's Permanent Representative to the EU at this crucial time.
"I look forward to joining the strong leadership team at the Department for Exiting the EU and working with them and the talented staff at UKRep to ensure we get the right outcome for the United Kingdom as we leave the EU."
The swift appointment follows demands from Labour for Brexit Secretary David Davis to face MPs over the controversy and for the Government to set out a clear timetable for the publication of its Brexit plan.
While many Leave supporters welcomed Sir Ivan's decision, others expressed concerns the experienced diplomat's departure could leave the Government in a weakened position as it works to agree an exit deal with Brussels.
Jonathan Powell, Tony Blair's former chief of staff, earlier told Sky News Britain would now be "going into the negotiations playing with a junior team if we are lucky".
Foreign Secretary Boris Johnson said Sir Tim was "just the man" to get the best deal for the UK, while Brexit Secretary
David Davis said his knowledge of Brussels meant he would "hit the ground running".
Labour, meanwhile, said "fundamental questions" about the Government's Brexit strategy "remain unanswered".
Meanwhile, an Irish MEP is calling for a new approach to Brexit by all parties concerned.
Sean Kelly told Newstalk it will be impossible to reach an agreement on every aspect of the break-up in 18 months, and is calling for a transitional arrangement between the E.U. and Britain by the end of 2018, with more room for both sides to negotiate the finer points of the deal later.
Mr Kelly says the longer period of withdrawal could have many benefits.
"All the indications are that even right now the majority of people, if they got the chance again, they would vote to remain", he said.