The decision follows a cataclysmic week in UK politics that also saw Nigel Farage step down as UKIP leader in a move that saw him branded the "latest rat to jump off a sinking ship".
Meanwhile a high-profile law firm has taken on the UK government over Brexit, saying enacting such changes without an act of Parliament could leave the decision open to legal challenges.
Mischo de Reya has put the case to government lawyers on behalf of an anonymous group of British citizens for an undisclosed amount.
The firm insists it is not a case of "sour grapes" and it has no interest in overturning the result but the decision to trigger Article 50 "rests with the representatives of the people under the UK Constitution".
Lawyers Baron David Pannick QC, Tom Hickman, Rhodri Thompson QC and Anneli Howard have been in contact with government lawyers since June 27. They want to ensure the government will "uphold the UK constitution and protect the sovereignty of Parliament" when considering the move.
It claims if Brexit legislation is not approved by parliament, the decision to withdraw could be "unlawful". That would "negatively impact" future relationships with the EU and 27 states leaving them open to "legal challenge".
Partner Kasra Nouroozi said: "We must make sure this is done properly for the benefit of all UK citizens."
"Article 50 simply cannot be invoked without a full debate and vote in Parliament. Everyone in Britain needs the government to apply the correct constitutional process and allow Parliament to fulfil its democratic duty."
The news comes as shock waves from the June 23 decision to leave the European Union continue to rupture British society.
The Conservatives, Labour and UKIP are now in turmoil over who will lead their parties creating an extraordinary leadership vacuum at a time of huge uncertainty for the country and its people.
Mr Farage's decision to step down has highlighted a major criticism of the Leave campaign - that it did not have a plan following the Brexit result.
Over the weekend former prime minister Tony Blair suggested there could be a second referendum and people should "keep their options open".
"One of the reasons why we should keep our options open is that yes, the referendum expressed the will of the people - but the will of the people is entitled to change," the Remain advocate told Sky News.
"The odd thing about the referendum was we knew what we were getting out of, (but) we don't know what we're getting into.
"As that becomes clear, if it's clear that these terms are bad for us, if we have major parts of business and the financial sector saying look this is not a good deal for us, if people start to worry about their jobs, we should just keep our options open."
It comes as comments made by Conservative leadership contender Andrea Leadsom in 2014 resurfaced in which she said "out" might not really mean "out."
"What we fail to consider is what 'out' really means," she said at the time.
"If Britain votes to leave the EU, we haven't left: we start negotiations. That set of negotiations to leave may even be more fruitful than the negotiations before the referendum."
On Monday Ms Leadsom committed to guaranteeing the rights of "our EU friends who have come here to live and work".
"We must give them certainty there is no way they will be bargaining chips in our negotiations," she said.
