"They can not keep on just regurgitating what has already been emphatically rejected three times by Parliament, there's got to be a change".
The pressure to end the Brexit deadlock comes as next month's European elections loom over May, with recent polls showing Nigel Farage's new Brexit party storming ahead of the Tories and his former party, Ukip.
Mrs May has come under heavy criticism for her handling of the Brexit process, but survived a vote of confidence by her MPs in December.
Candidates for the party, which is calling for a new referendum on Britain's European Union membership, include the former BBC broadcaster Gavin Esler and journalist Rachel Johnson, sister of Boris Johnson.
It's worth noting that the European Union (EU) granted a six-month extension until Oct 31st to the United Kingdom government to leave the EU after as May failed to break an impasse in parliament on the terms of Brexit. The petition points out that the promised exit from the European Union has been delayed twice, branding her the wrong person to negotiate the deal with other bloc member states. The country will now not withdraw from the bloc potentially until Oct 31, prolonging the political uncertainty, to the dismay of business leaders.
"What we are hearing on the doorstep is the anger at both the main parties".
Farage castigated Labour for, as he put it, reneging on its promise to support Brexit, saying: "We're going to go after that Labour vote in a very big way".
Mrs May's official spokesman told reporters: "The Prime Minister said discussions with Labour had been serious but had also been hard in some areas, such as in relation to the timetable for the negotiations".
The party - formerly known as The Independent Group - is made up of 11 MPs who quit Labour and the Tories.
Mrs May said the United Kingdom could still exit before this date if her withdrawal agreement is approved by Parliament.
Some 70 local Conservative association chiefs have signed a petition calling for an extraordinary general meeting of the National Conservative Convention to discuss the Prime Minister's leadership of the party.
She told the BBC: "I'm afraid the prime minister is conducting negotiations in such a way that the party does not approve".
Claire Fox, who now styles herself as a libertarian and is a panellist on BBC Radio 4's Moral Maze programme, told the launch event she most likely only agreed with Farage on one issue - Brexit.
After the Easter break, however, May seems keen to renew talks, to avoid humiliation at the polls next month, when Britain has local elections in addition to the scheduled European elections.