The YouGov poll for the Times, conducted over past two days (May 30-31), puts the Tories on 42 per cent with the Labour party close behind on 39 per cent.
The Tories' three point lead is the lowest of the campaign so far, while Labour’s 39 per cent is the party’s highest poll result since February 2014.
Theresa May's hopes of winning a bigger Commons majority are under threat
The YouGov poll is just the latest which shows the gap between the two main parties is closing, with the Tories 18 points ahead of Labour when the snap General Election was called on April 18.
The pollster, who garnered responses from 1,875 British adults, put the Lib Dems down two points on seven per cent, with Ukip behind on four per cent.
There’s more bad news for the Prime Minister too – her personal poll approval lead over Jeremy Corbyn has shrunk to 13 points, a four point drop from the end of last week.
The TV election debate – in pictures Wed, May 31, 2017
The televised debate saw Jeremy Corbyn, Amber Rudd, Paul Nuttall, Caroline Lucas, Angus Robertson, Tim Farron and Leanne Wood go toe-to-toe
PA 1 of 15
The politicians taking part in the debate
Mrs May’s decision not to appear on Wednesday evening’s leaders’ debate is unlikely to be popular with voters, with Home Secretary Amber Rudd representing the Conservatives in the Prime Minister’s absence.
Party leaders accused Mrs May of lacking “guts” and “running away from the debate” during the 90-minute programme.
Lib Dem leader Tim Farron launched a string of attacks on Mrs May. He said: "Where do you think Theresa May is tonight?
Get Quotes on Home Insurance
Amber Rudd stood in for Theresa May as the Tories' representative for the debate
"Take a look out your window. She might be out there sizing up your house to pay for your social care."
Meanwhile, Green party co-leader Caroline Lucas said the "first rule of leadership is to show up".
She added: “You don't say it's the most important election of our lifetime and not be bothered to show up."
Theresa May defended her decision not to appear at the BBC debate
Plaid Cymru leader Leanne Wood added that Mrs May was absent because "her campaign of soundbites is falling apart".
Yesterday, a different YouGov poll predicted the Conservatives will fall 16 seats short of an overall majority. The polling method has taken into account an unusual technique using a complex computer model.
The YouGov prediction would leave Theresa May with 310 MPs – 20 fewer than at the time of dissolution of the last Parliament – while Labour are set to surge from 229 to 257 MPs on June 8 election, a gain of 28 seats in the Commons.
Snap election 2017: The pictures politicians may not want you to see Sat, May 27, 2017
Protests, fights and daleks, it's all happening as the politicians hit the campaign trail for the snap election
PA 1 of 48
Jeremy Corbyn during a visit to Hackney Marshes Football Pitches, to highlight Labour's manifesto commitment to ensure 5% of the Premier League's television rights income is diverted to the grassroots game, during a General Election campaign
The shocking scenario could leave Theresa May’s hand weakened ahead of Brexit negotiations – or see her ousted by an opposing coalition government.
While a number of pollsters have projected a declining lead for the Conservatives, YouGov’s three point margin is the lowest.
A recent ICM poll showed a three-point lead until it was adjusted according to its turnout model which increased the Tories’ lead by eight points, according to YouGov.