International Trade Secretary Liam Fox said Labour's proposals were "not workable" while Boris Johnson accused Mr Corbyn of trying to trap the Government in a "toxic" Brexit.
Theresa May has effectively ruled out Labour's ideas for a compromise Brexit plan, shutting off another potential route to a deal as business groups warned that with less than 50 days to go the departure process was entering the "emergency zone".
The Prime Minister's official spokesman said it would give MPs more time to "digest the content" ahead of a series of expected Commons votes on Thursday.
Mrs Leadsom said there was "no chance" Mrs May would adopt Mr Corbyn's "view of the world", adding: 'The Prime Minister has been absolutely clear we're leaving the EU, we're leaving the customs union, we're leaving the single market'.
Mrs May told the Labour leader: "It is good to see that we agree that the United Kingdom should leave the European Union with a deal and that the urgent task at hand is to find a deal that honours our commitments to the people of Northern Ireland, can command support in Parliament and can be negotiated with the EU - not to seek an election or second referendum".
Negotiations of a kind have also been taking place back in Westminster, with an exchange of letters between Mrs May and Labour leader Jeremy Corbyn.
Labour MP Lisa Nandy told the BBC's Politics Live that there were between 40 and 60 of her colleagues "who are actively looking for ways to support" a revised Brexit deal.
"He now wants to frustrate Brexit very largely by staying in a permanent customs union".
Mr Fox, in Bern for the signing of a trade agreement with Switzerland, said Labour claims they would be able to influence European Union trade policy showed they did not understand how European Union policy worked.
Mrs Leadsom said: 'I think she's making quite clear that what Corbyn is demanding is actually not as good as what the Prime Minister's deal is offering.
That leaves May battling to persuade a reluctant European Union to look again at the Irish backstop - a fallback policy created to prevent the resurrection of a hard border in Ireland if talks to find a long-term trade arrangement fail.
Jeremy Corbyn said he believes Theresa May might try to run out of the clock on a Brexit deal.
"I'm certain of one thing, is that it's not going to be as good as if they had not been Brexit, that is for sure", Lagarde said.
"I think that you would need to have a time limit".
Mr Barclay will later travel to Brussels for talks over dinner with the EU's chief negotiator Michel Barnier. Although lawmakers asked for the backstop to be removed, May has said since that the backstop will remain, and that Parliament merely asked for it to be altered.
Mrs May wants the two parties to discuss how "alternative arrangements" to the Irish backstop - a commitment to avoid a hard border - could work.