The ORB/Telegraph poll of 800 people showed support for remaining in the EU stood at 55 percent, up 4 percentage points since a comparable poll last month, while the number backing Brexit, as leaving is known, was down 3 percentage points to 40 percent.

The survey helped send sterling to a 2-1/2-week high against the euro.

"Time may be running out for the "Leave" camp to make the case for Brexit as the "Remain" campaign's position is consolidating and the electorate becoming more polarised," Lynton Crosby, the strategist who helped Prime Minister David Cameron win last year's national election, wrote in the newspaper.

But Crosby said the biggest challenge for Cameron's campaign to keep Britain in the EU was to get pro-European voters out on polling day. The ORB survey found among those who would definitely vote 51 percent backing "remain" and 45 percent supporting "leave".

"Turnout continues to be a major issue for the Remain campaign," Crosby said.

Opinion surveys, which failed to predict Cameron's unexpectedly decisive victory in Britain's 2015 national election, have given a contradictory picture of Britons' voting intentions ahead of the June 23 referendum.

ICM released two polls on Monday with starkly different pictures of British opinion. A telephone poll showed the "In" campaign ahead on 47 percent while an online poll showed "Out" ahead on 47 percent support.

Betting odds have consistently indicated a vote to stay in the 28-member bloc and the implied probability of an in vote rose to 73 percent on Tuesday, according to Betfair odds.

A British exit from the EU would rock the Union - already shaken by differences over migration and the future of the euro zone - by ripping away its second-largest economy, one of its top two military powers and by far its richest financial centre. 

DIFFERENT POLL SHOWS OUT IN THE LEAD

Meanwhile, polling firm TNS said the campaign to get Britain out of the European Union has taken a three-point lead over the "Remain" campaign, the first time it has found the "Out" campaign ahead since February.

Forty-one-percent of respondents wanted Britain out of the EU, up five percentage points from a May 3 poll, while those wanting to remain in the bloc fell one point to 38 percent.

"This poll suggests that we are seeing movement from undecided voters towards the Leave camp, though we will need to wait until the next poll to see if this is a trend or random variation," Luke Taylor, head of social and political attitudes at TNS UK, said.

"Although this poll is the first time since February that we have seen a lead for 'Leave', the race remains very tight with many yet to make up their mind."