LONDON (Reuters) - The gap between Britons who want to remain in the European Union and those who want to leave remains tight ahead of a membership referendum due by the end of 2017, according to two opinion polls on Monday.

Prime Minister David Cameron has promised to renegotiate Britain's relationship with the bloc ahead of the vote. He has said he wants Britain to stay in a reformed EU but rules nothing out if he cannot get the changes he wants.

A YouGov survey of 2,781 adults, carried out Sept. 17-22, found 41 percent would vote to leave, while 38 percent favored staying and 17 percent were undecided.

But a separate Survation poll of 1,008 adults, carried out Sept. 21-22, found the 'in' camp slightly in the lead, with 43 percent saying they wanted to stay and 40 percent backing leaving. It also found 17 percent were undecided.