Brexit backers led the polls Monday for the first time in weeks, putting pressure on the pound and Prime Minister David Cameron just over two weeks before Britain's EU referendum.
The WhatUKThinks average put "Leave" at 51 percent against "Remain" at 49 percent ahead of the June 23 vote that the pro-EU camp says could see financial markets plunge and hit global economic growth if Britain votes to go.
The balance tipped in favour of "Leave" following three polls over the weekend, and on Monday showed a growing number of Britons want their country to become the first to break away from the EU.
The last time the average put "Leave" ahead was on May 12.
The swing comes just days after Brexit campaigners unveiled plans for an Australian-style points-based immigration system if they win.
"We have absolutely no control over the people coming from the whole 27 other EU countries, some of them with criminal records," said former London mayor and leading Brexit advocate Boris Johnson at a campaign event on Monday.
"So what we need is a system that is balanced, fair, but, of course, remains open to talent. We are talking about taking back control of our immigration policy," he said.
The influx of EU workers from countries such as Italy, Poland, Romania and Spain is at near-record highs and anti-EU campaigners say the new arrivals drive down salaries and burden public services.
Cameron, who heads up the "Remain" camp, has promised to curb immigrant numbers and has warned of the economic risks of leaving.
He took part in an event Monday with political opponents Labour, the Liberal Democrats and the Greens to accuse "Leave" supporters of "perpetuating an economic con-trick on the British people".
"While they peddle fantasy politics, in the real world our economy is slowing because of the huge uncertainty hanging over Britain's economic future," Cameron said at the "Britain Stronger In" event.
The broadside came after Johnson, a charismatic politician with popular appeal who is seen as the most likely successor to Cameron, warned Britain would have to pay more for membership of the EU.
"The risks of 'Remain' are massive," he said.
Former Conservative prime minister John Major on Sunday made a scathing personal attack on Johnson, describing him as a "python" who could not be trusted.
Financial markets have proved volatile ahead of the vote, particularly as the campaign has heated up.
The pound fell to 79.05 pence against the euro in Asian trading -- its lowest level in three and a half weeks -- and stood at around 78.78 pence against the euro at around 1300 GMT.
The pound also fell against the dollar to $1.4401 -- a three-week low.
"It is becoming extremely worrying for the financial markets and expect more sterling losses if polls continued to indicate a Brexit lead," said Hussein Sayed, chief market strategist at trader FXTM.
Craig Erlam, senior market analyst at Oanda, said: "With both sides likely to step up their game over the next couple of weeks, I imagine we'll see a lot more volatility in the pound."
Several of the biggest trade unions also urged members to vote to stay in the EU.
The general secretaries of Unite, Unison and the GMB were among 10 union leaders who wrote a letter to The Guardian newspaper claiming that parental leave and holiday rights would be under threat from the Conservative government without EU protection.
"Maternity and paternity rights, equal treatment for full-time, part-time and agency workers and the right to paid leave -- continue to underpin and protect working rights for British people," read the letter.
"If Britain leaves the EU, we are in no doubt these protections would be under great threat. The Tories would negotiate our exit and, we believe, would negotiate away our rights," it said.