Prime Minister David Cameron is setting off Thursday on a whirlwind visit to four European capitals, pressing his case that Britain needs to renegotiate its relationship with the 27 other members of the bloc.

The trip began as Cameron's government revealed the question British voters will be asked in a referendum by the end of 2017: "Should the United Kingdom remain a member of the European Union?"

Cameron said Wednesday that he expected the referendum bill to make it through Parliament and into law in "extra quick time."

He wants Britain to stay in the EU, if he manages to negotiate a new, looser relationship with the group.

"We believe the right policy is reform, renegotiation and referendum," he said, expressing confidence that Britain's bid for a new relationship with the EU would succeed.

Cameron plans to travel to the Netherlands, France, Poland and Germany on Thursday and Friday as part of his efforts to talk with all of the leaders of the EU member states before a European Council meeting late next month. A planned trip to Denmark was cancelled because Prime Minister Helle Thorning-Schmidt declared an election.

On Thursday, Cameron will meet Dutch Prime Minister Mark Rutte for a working lunch followed by talks at the Elysee Palace with French President Francois Hollande. On Friday, he meets with Polish Prime Minister Ewa Kopacz in Warsaw before traveling to Berlin for talks with German Chancellor Angela Merkel.

European leaders have expressed a desire to accommodate Britain, but it's unclear how far they will go to meet Cameron's desire for change — especially to the right of EU citizens to live and work anywhere in the bloc.

"I hope in the U.K. there is a debate that also respects how far Europe can go to meet it," German Foreign Minister Frank-Walter Steinmeier said Wednesday.

Britain's referendum proposal will allow British, Irish and Commonwealth citizens to vote in the referendum, but not most citizens of other EU states.