British support for staying in the European Union has fallen by two percentage points to 51 percent according to a poll, a decline that may suggest U.S. President Barack Obama's words in favor of UK membership had yet to have an impact.

Support for leaving the 28-member bloc in a referendum has increased by 2 percentage points to 43 percent in the past week, little changed from figures published on April 19, according to the ORB poll of 800 people for The Daily Telegraph newspaper on Tuesday.

Several agencies and David Cameron's advisers are polling voters almost continuously on their plans for a referendum on June 23 on EU membership, a vote that will determine the prime minister's future and that of the country in world affairs.

But some have cast doubt on the results of the research, after the polling industry suffered a blow to its credibility last year when it failed to predict the Conservative Party's outright victory in a general election.

Lynton Crosby, an election strategist who helped Cameron win last May's election, said the Telegraph's poll showed "not much has changed over the past week" despite Obama on Friday urging Britons to remain in the bloc.

"The effect of the president's visit may not yet be felt in the numbers as sometimes it takes a while for factors to wash through. Also, people may not take much notice of what an outsider has to say," he wrote in The Telegraph.

While on a visit to London, Obama said Britain would be at "the back of the queue" for a trade deal with the United States if it voted to leave the EU, a warning that sparked anger amongst those campaigning to leave the EU.

Crosby said the "In" campaign was at risk of "voter complacency" -- almost three fifths of voters polled said they believed those campaigning to stay in the EU will win and may not then feel it necessary to turn out to vote.

"Who is leading at this stage may be indicative of what is yet to come, but the road ahead remains fraught," Crosby said.

"I wouldn't be hanging out the victory bunting just yet. The marathon has barely begun."