Cross-party Brexit talks were believed to be close to collapse last night after Downing Street firmly rejected demands for any compromise deal to include a referendum that could keep the United Kingdom in the EU.
The Brexit Party leader said he would also be prepared to do a deal "with the devil", including a Conservative leader, if it meant Britain left the European Union on World Trade Organization (WTO) terms.
He said: "The talks clearly aren't getting anywhere".
Addressing a party rally in west Yorkshire, Farage said that up until the European elections, where his party leads in the polls, he would talk only about Brexit-related matters.
The beneficiaries of a collapse in support for the Tories in London appears to be the Brexit party, which from a standing start is polling in second place.
It is on for a predicted 34 per cent of the vote on May 23 - but Theresa May's Conservatives are heading for just 10 per cent, a new YouGov survey has found.
"The pressure on Prime Minister May to resign mounts, but attempts to remove her from her function have failed so far".
If Prime Minister May had managed to persuade a majority parliament to back a withdrawal deal she negotiated after two years of ill-tempered talks, Britain wouldn't be holding the May 23 elections.
British Foreign Secretary Jeremy Hunt said European Union leaders did not want an extension beyond the new deadline of October 31, when the legal default is to leave with or without a deal.
The inability to agree on a way forward led the United Kingdom to miss its 29 March deadline for leaving the European Union - the current date for departure is 31 October. But as the cabinet and shadow cabinet take stock of the progress so far in the cross-party talks, pressure is mounting on both sides for negotiations to be abandoned.
She argued that while they shouted over each other there had been a "wide-ranging debate" and the result of the referendum had also been "endorsed" at the 2017 elections.
Corbyn's aides say he's trying to ensure the support of the third of Labour supporters who favor Brexit.
After a marathon Cabinet meeting earlier on Tuesday, ministers agreed to continue the cross-party efforts to break the impasse but stressed it was "imperative" for a Brexit deal to get through Parliament by the summer recess.