The Tories would only win 28 per cent of the vote if a general election were held tomorrow, with Labour earning 32 per cent of votes, according to a YouGov poll for The Times.
They are also set to do badly in the European Pariament elections due on May 23rd, in which the party has slipped into third place among those who voted to leave the EU, behind UKIP and Nigel Farage's new Brexit Party.
An Opinium poll published in the Observer newspaper showed the Conservatives at 29 percent, down 6 points from March 28 and 7 points behind Labour.
The British government will resume talks with the main opposition Labour party next week on how to resolve the deadlock over Brexit, a senior minister said Sunday. He described the delay to Brexit as "political death" and urged May to avoid taking part in the European elections.
These will be used to gauge the electoral impact that failing to deliver Brexit on schedule has had on May's Conservative Party.
The minister for the cabinet office explained that while the two parties have common goals there needed to be movement from both sides.
The ERG Chairman said he thought that it was "noticeable" of how much appeal Boris Johnson has with voters beyond the Conservative Party and eurosceptics.
In a potential European Parliament election, Labour would lead with 24 per cent, followed by the Conservatives on 16 per cent, the Brexit party on 15, UKIP on 14, the Lib Dems and Greens scoring 8 per cent each, and Change UK on 7 per cent, the poll claimed.
"What the prime minister has to do now is aim everything towards departure before the euros (European elections) which would then allow her to step away having done what she said she would do - get the United Kingdom out of the European Union one way or the other", he told Sky News.
Britain's exit from the European Union was postponed by a late night agreement in Brussels last week that gave Prime Minister Theresa May until Oct 31 to persuade parliament to approve the terms of the country's departure.
Mrs May has also faced criticism for agreeing to negotiate a Brexit deal with Labour leader Jeremy Corbyn.