Barry Gardiner, Shadow Secretary for International Trade, also called on Mrs May to make way for a Labour Government if she is unable to secure a final Brexit deal within Parliament, pushing the UK towards a ‘no deal’ outcome.
Speaking on ITV Peston, he said: “It is a hierarchy. First we have to have an agreement with the EU, we will then vote on that, and if she cannot get that through Parliament, that puts the country in jeopardy by putting us on track for a ‘no deal’.
“If she gets us to that chaos where there is ‘no deal’, that there is no agreement in the British Parliament and we are heading off the cliff of ‘no deal’, then it is absolutely right that she should make way.
“Then we will say, if you cannot get anything through Parliament, if you can’t govern, make way for a party that perhaps can go back to Europe and govern and get that agreement.”
However, in a stark criticism of Mrs May and the Conservative Party, he added: “Do I think she’s got the decency to do it, do I think the Conservative Party has the decency to do it? I doubt that very much and so do most people.”
Mr Gardiner instead praised Labour leader Jeremy Corbyn for striking a conciliatory tone with the EU, and vowing to compromise over key issues in a bid to secure a viable Brexit deal.
Referring to Mr Corbyn’s speech at the Labour Party conference in Liverpool on Wednesday, Mr Gardiner said: “What Jeremy did today was seizing the initiative, saying to the country, ‘look, we want to work together in the interest of the country to get a deal, it’s not perfect, but we certainly don’t, surely for goodness sake, want a ‘no deal’ that will take us over the edge of that cliff’.
“It means compromising. If it means you bending your red lines to give us a customs union, we’re prepared to bend our red lines to get a deal.
“Jeremy has tried to act in way that respects the referendum result, but by doing minimal damage to our economy.”
He argued that a viable solution still exists in order to achieve a deal which will be accepted both by the EU and Parliament.
The Labour politician pointed to a customs union with the EU as a viable solution to the ongoing Brexit deadlock.
He said: “That is our party policy and has been for over a year.
“Let’s go back to what Jeremy said earlier today, it is a customs union, but we all need to know and be sure that all the things we have said about rights, worker rights, holiday pay, holiday leave, maternity pay, maternity leave, are guaranteed so that we are not reducing our standards.
“Now the Government can promise this, but we need to see all of this in the back deal.”
Mr Gardiner warned that if Mrs May fails to conclude a Brexit deal which protects UK standards, or which pushes the UK towards a ‘no deal’ outcome, Labour will reject her proposal in Parliament.
In a damning conclusion, he said: “If Theresa may does not do that, if she does not come back with an acceptable deal, if it is a fudge, we will not vote for it.”