LONDON (REUTERS) - The number of Britons who would back staying in the European Union at a planned referendum has fallen after the government agreed to amend the wording of the question to be put to voters, a poll showed on Tuesday.

Prime Minister David Cameron has promised to renegotiate Britain's ties with the EU before a membership referendum by the end of 2017.

Earlier this month, the government said it would change the wording of the question, which some had argued favoured the 'in'camp, after a recommendation from Britain's elections watchdog.

When asked the modified question, the poll carried out on Sept 11-13 by pollster ICM found 43 percent of the 2,006 adults surveyed backed Britain's continuing EU membership, while 40 percent would opt to leave.

Its previous poll, which asked people the old question a week earlier, found 45 per cent wanted to stay in the bloc and 37 per cent favoured leaving.

Under the government's initial proposal, voters were to be asked to say "yes" or "no" to the question "Should the United Kingdom remain a member of the European Union?" Some who want Britain to leave the 28-member bloc argued that was unfair because it would allow the campaign to stay in the European Union to brand itself as the more positive "yes"camp.

The question has now been changed to "Should the United Kingdom remain a member of the European Union or leave the European Union?"