Gardiner, a former aide to Margaret Thatcher, said a second referendum would be a "slap on the face" to the estimated 17.4 million British people who voted to leave the EU.
It followed more than two years of political upheaval in which May has staked her political reputation on getting a Brexit deal and was the biggest defeat for a government in the House of Commons in modern history.
The motion was tabled tabled on Tuesday by Labour leader Jeremy Corbyn after 432 MPs voted against the Brexit deal.
But senior Labour figures accept it is not likely to succeed, as she has the backing of Tory rebels and the DUP's 10 MPs, who less than 24 hours ago helped inflict a humiliating defeat on her.
May's Brexit agreement was created to keep trade rules between the world's fifth-biggest economy and its largest export market nearly unchanged for a transition period running through the end of 2020.
One remote possibility is that May's own Cabinet may turn against her, telling the prime minister that it has lost confidence in her leadership and that she should step down.
Sterling was changing hands at $1.2848, slightly below $1.2860 seen late Tuesday in NY.
Foster added: "Whilst some may wish to use this defeat to boost their political ambitions, we will give the government the space to set out a plan to secure a better deal". Parliament has given the government until Monday to come up with a new proposal.
European Commission president Jean-Claude Juncker returned Tuesday to Brussels to deal with Brexit issues arising from the vote, amid signals May might be heading back to EU headquarters on Wednesday.
The other options on the table are a second referendum, a renegotiation with the European Union or an European Union departure without a deal.
May suffered the biggest government defeat in modern British history on Tuesday night when the House of Commons rejected by 432 votes to 202 the withdrawal agreement she struck with Brussels late previous year.
However there was a ray of hope that a Brexit crisis could be averted as on Wednesday EU's chief negotiator, Michel Barnier, said that if May shifted on her red lines, the EU was open to renegotiation.
Prince Harry and Meghan Markle will attend Cirque du Solei in London
Meghan rescued her dog Guy from a shelter in 2015 and she and Harry are believed to have adopted a second pup previous year . The Duchess is a proud dog lover, having previously supported various animal rescue centres in her home city of Los Angeles.
"That's why I am inviting MPs from all parties to come together to find a way forward". "Things have now got to change, starting with the government", the party's Brexit spokesman Keir Starmer said in a video message on Twitter. His party wants a permanent customs union with the EU, a close relationship with its single market and greater protections for workers and consumers.
"The Brexit deal is basically dead", said Anand Menon, professor of European politics and foreign affairs at King's College London.
"I urge the United Kingdom to clarify its intentions as soon as possible".
"Time", Junker added, "is nearly up".
Scores of her own MPs - Brexiteers and supporters of European Union membership alike - joined forces to vote down the divorce deal.
The prime minister said an election was "simply not in the national interest".
Carney said the increase was to preserve the ability of banks to lend in the midst of a crisis and to keep Britain attractive to global investors.
"Good luck to the representatives of the nation who have to implement something that doesn't exist", Macron said. Brookings' Amanda Sloat has been tracking the Brexit process closely; in previous posts, she has explained what May's plan entails, the revolt within her party, and why the plan didn't get a vote in December.
Business groups had appealed for lawmakers to back the deal to provide certainty about the future.
The deal was doomed by deep opposition from both sides of the divide over the UK's place in Europe.
"Were the backstop to enter into force in whole or in part, it is meant to apply only temporarily, unless and until it is superseded by a subsequent agreement", Tusk and Juncker added, pledging the "necessary political impetus and resources" to quickly reach that more permanent agreement.