The Survation poll places the Conservatives on 42%, with Labour on 40%. The Liberal Democrats are on 6%, with Ukip on 3%.
At the beginning of May, the Survation poll had Conservatives on 47% and Labour were lagging behind on 30% - a 17-point deficit.
The polling company also revealed other data, such as 51% of people polled thought Labour had run the best campaign so far. Just 23% of those surveyed thought the Conservatives had run the best campaign.
Three-quarters of those interviewed did not believe Theresa May would achieve her pledge to reduce net migration to the tens of thousands, including 29% of current Conservative voters.
Survation also found: “While the public were generally split over whether they approve or disapprove of the possible government formations listed if there was no overall majority, people would rather one of the main parties governed alone as a minority government rather than forming a coalition.”
The company interviewed 1,103 UK residents aged 18 and over by telephone on June 2 and 3. Data was weighted to be representative of all UK adults.
Clashes over cuts to the police services rumble on today, with Sadiq Khan warning the Met faced having to make savings of £400m if the Conservatives win the election, risking up to 12,800 officers.
Foreign secretary Boris Johnson told the Today radio programme the Conservatives were putting more money into counter-terrorism.
Johnson also told the Radio 4 listeners there was “no reason” to cancel the US president Donald Trump’s visit to Britain later this year, which Khan has called for.
The foreign secretary did, however, back Khan’s reassurance to Londoners that more armed police officers on the streets was nothing to be alarmed about.
Home secretary Amber Rudd has denied a drop in police officers numbers by 20,000 between 2010 and 2016 contributed to the terrorist attack in Manchester last month.
