Hartlepool MP Mike Hill says it is time to 'crack on with leaving the EU' after the latest House of Commons votes on Brexit.
In a dramatic night of votes in the Commons, MPs supported a proposal endorsed by the Prime Minister to reopen the Withdrawal Agreement and replace the backstop with "alternative arrangements" to avoid a hard border in Ireland.
But she earned an immediate rebuff from Brussels, where European Council president Donald Tusk insisted that the Withdrawal Agreement struck last November was not open for renegotiation.
Meanwhile, one of Mrs May's strongest negotiating weapons was ripped from her hands by MPs who voted to block a no-deal Brexit.
The Commons voted by 317 to 301 in favour of the backstop changes - which Mrs May said showed there was a means of securing a "substantial and sustainable majority in this House for leaving the EU with a deal" and vowed to seek a new agreement with Brussels.
Town MP, Mr Hill says it is time to focus on a deal that 'removes red lines, protects people’s rights, the economy, business, the environment, public services and local jobs'.
Mr Hill posted on Facebook after the vote last night: "No deal Brexit clearly not the will of Parliament nor is a second referendum after today’s votes.
"Focus is now to crack on with leaving the EU with a deal that removes red lines, protects people’s rights, the economy, business, the environment, public services and local jobs.
Theresa May is preparing to return to the EU to try to renegotiate her Brexit deal after MPs gave their backing to proposals to replace the controversial backstop.
But in a statement, Mr Tusk's spokesman said: "The Withdrawal Agreement is and remains the best and only way to ensure an orderly withdrawal of the UK from the European Union.
"The backstop is part of the Withdrawal Agreement, and the Withdrawal Agreement is not open for re-negotiation."
The EU's chief Brexit negotiator, Michel Barnier, told reporters in Brussels: "The position of the European Union is very clear."
Irish foreign minister Simon Coveney said the controversial backstop arrangement remained "necessary" despite the vote, while the European Parliament's chief Brexit negotiator, Guy Verhofstadt, said there was "no majority to re-open or dilute" the Withdrawal Agreement.
And French President Emmanuel Macron also said the agreement was "not renegotiable", in comments just moments before MPs voted.
While Foreign Secretary Jeremy Hunt said the Conservatives had shown they "can and will come together in the national interest", signs of division in the party remained as Tory former minister Anna Soubry said she finds her "party drifting to the right".
The Commons approved a cross-party amendment, tabled by Midlands MPs Caroline Spelman and Jack Dromey, rejecting a no-deal Brexit by 318 to 310.
The vote is not legally binding on the Government but will impose massive political pressure on the Prime Minister to delay Brexit from its scheduled date of March 29 if she cannot secure a new deal from Brussels.
Mrs May told MPs: "I agree that we should not leave without a deal. However, simply opposing no-deal is not enough to stop it.
"The Government will now redouble its efforts to get a deal that this House can support."
There was uproar in the chamber as she said: "There is limited appetite for such a change in the EU and negotiating it will not be easy. But in contrast to a fortnight ago, this House has made it clear what it needs to approve a withdrawal agreement."
Mrs May said she would seek "legally binding changes to the Withdrawal Agreement that deal with concerns on the backstop while guaranteeing no return to a hard border".
And she told MPs: "If this House can come together, we can deliver the decision the British people took in June 2016, restore faith in our democracy and get on with building a country that works for everyone.
"As Prime Minister I will work with members across the House to do just that."
Tuesday's votes were triggered by the overwhelming defeat of Mrs May's Brexit Plan A by 230 votes earlier this month.
Labour leader Jeremy Corbyn, who boycotted cross-party talks after that vote, said that he was now ready to meet the Prime Minister to discuss a "sensible Brexit solution that works for the whole country".