Some 43% said Mrs May should resign now and 33% once a Brexit deal has been reached - the timetable the Prime Minister has indicated for her departure.
Announcing her candidature to become an MEP representing the South West region for the Change UK - The Independent.
Change UK interim leader Heidi Allen told the event that 3,700 people had offered to stand as party candidates in the European elections.
Ahead of the launch in Bristol, she told BBC Radio 4's Today programme the candidate list was made up of former members of the Tories, Labour, Liberal Democrats and Greens - as well as some non-political individuals - and people were starting to call them "the Remain Alliance".
Elizabeth Warren releases sweeping student debt cancellation and free college plan
Broadly speaking, forgiving student loan debt would provide a helping hand to the one-third of Americans who have college degrees. When it's all said and done, about 95 percent of borrowers will see a reduction in their student-loan debt.
It is just one of the calls that will be facing her from MPs, councillors and party workers after a hard two weeks of campaigning on the doorsteps of the country.
"These elections are a chance to send the clearest possible message - we demand a People's Vote and the right to campaign to remain in the European Union".
Additionally, 40 percent of her own advisors are said to be ready to back Nigel Farage's Brexit Party.
She said it was treating its first test at the ballot box "very, very seriously indeed", as the campaign itself would "send the loudest possible message to both the government and the opposition about how people in the United Kingdom feel about leaving and the deal that is now on the table".
'I have never been seriously anxious about the future of our country but I am now. "It is a worldwide joke", he told the event.
Trump on Impeachment Talk: Dems Committed Crime
Congress, however, has much more freedom of action in responding to the Mueller Report . Lee said, "There's nothing in this report that changes my view of this president".
"Our political system is a joke".
"The bigger principle for people in Britain is that we voted to leave the European Union and they want the politicians to get on with it", he told the BBC Radio 4 Today program, adding that it would be " very, very challenging" for May to continue as leader if she failed to get her deal through.
Launched in January by Farage and former UKIP spokesperson Catherine Blaiklock, the Brexit Party was Britain's highest polling party in a poll last week by YouGov on the public's voting intentions for the European elections.
Other candidates standing for the Independent Group across Britain include former Tory MP Neil Carmichael, former Liberal Democrat MEP Diana Wallace and former Labour MP Jon Owen Jones, as well as the former finance minister of Poland.
Strong natural disaster shakes areas north of Philippine capital
The quake was centred on the town of Castillejos, about 100 kilometres (62 miles) northwest of Manila, local geologists said. She said 20 persons have so far been rescued from the collapsed supermarket and brought to the nearest hospital.