Opinion polls have highlighted the threat that the United Kingdom's Conservative party faces in both this month's European election and in a possible general election, piling more pressure on Prime Minister Theresa May to quit, the Financial Times reported.

A number of Conservative politicians and activists want May to resign as soon as possible, with the Brexit process having become more chaotic, three years since the referendum.

May's inability to get a deal through Parliament has fuelled anger among voters, Reuters reported.

The country's education minister said on Sunday that European elections will be difficult for Britain's governing Conservatives, as the party dropped into the fourth place in new polls that highlight a surge in support for the Brexit party.

Some Conservatives predict a disaster.

"The problem is the PM personally. Not her deal or her policies — her," FT quoted an unnamed Conservative candidate for the European elections as saying, adding that the mood on the campaign trail was "absolutely terrible".

"If she stands aside this week — that is, if the succession is already formally under way by polling day — there may be something for her successor to salvage. If not, we are looking at the end of the Conservative party," the person said.

The local elections earlier this month increased pressure on May, as the Conservatives lost more than 1,000 seats. It was the party's worst result in more than 20 years.

May has said that she would only step down when her deal is passed by Parliament.

May is expected to face pressure to set a departure date when she meets the executive of the Tories' 1922 committee of backbench members of Parliament on Thursday.

If the prime minister fails to commit on a timeline, the committee may seek to change its rule book to allow MPs to force a leadership election sooner than the current permitted date of Dec 12.

In two opinion polls on Sunday, the Brexit Party was set to come first in the European elections.

In a ComRes poll commissioned by Brexit Express, a pro-Leave organization, the Brexit Party led with 27 percent, with Labour on 25, the Liberal Democrats on 14, and the Conservatives on 13.

An Opinium survey found that 34 percent of people intend to vote for the Brexit Party led by Nigel Farage, with 21 for Labour, 12 for the Liberal Democrats and 11 for the Conservatives.

The ComRes survey also found that 27 percent of people would vote for the Labour party in a general election, with 20 percent for the Brexit Party, and 19 for the Conservatives.