(Reuters) - Support for Britain to stay in the European Union stood at 51 percent, five points ahead of support for a withdrawal from the 28-member bloc but down from a 13-point lead a week ago, an ORB poll for the Daily Telegraph said.
Support to leave the EU grew by 4 points to 46 percent according to the poll published on Monday for Tuesday's edition of the newspaper.
Britons vote on June 23 on whether to remain in the EU, with important implications for its trade, economic and political status.
Writing in the newspaper Lynton Crosby, the political strategist behind Prime Minister David Cameron's election victory, said the campaign focus on migration over the past seven days had boosted the Leave campaign.
"Increasing focus on lack of control over immigration" had helped to boost support for the "Leave" campaign, he said.
Two leading members of Cameron's ruling Conservatives have accused him of breaking his promise to curb immigration, stepping up hostilities in the party over a battle to win next month's referendum.
They pointed to official statistics issued last week showing net migration to Britain reached 333,000 in 2015, the second-highest level for a single year since records began in 1975. Of those, a net 184,000 came from the EU, which upholds the principle of free movement.
Immigration is a key focus in an increasingly bitter fight over EU membership, with many voters concerned about the strains a growing number of people put on schools, hospitals and housing.
Reporting by Ismail Shakil in Bengaluru and Elisabeth O'Leary in Edinburgh; Editing by Diane Craft and Sandra Maler