UPDATE 1-UK PM says referendum best solution for EU relations

(Adds detail, background)

BIRMINGHAM, England, Oct 9 (Reuters) - Prime Minister David Cameron said on Tuesday a referendum on Britain's relationship with the European Union was the most sensible way of forging a fresh settlement with the 27-member bloc.

Cameron is under mounting pressure from his party's restive right wing for a vote on Britain's relationship with the European Union. Cameron says Britain should remain in the union.

Cameron gave no time frame for a vote or any indication of what could be asked at such a referendum. The prime minister has said he is against a simple in/out referendum.

"When we achieve that fresh settlement it needs consent, either at a referendum or a general election," Cameron told the BBC on the sidelines of the Conservative Party conference in the English city of Birmingham.

"Frankly a referendum is obviously the cleanest, neatest and most sensible way of doing that," he said.

(Reporting by Mohammed Abbas and Guy Faulconbridge)