The Conservative Party’s victory in the U.K.’s May 7 general election reflected Prime Minister David Cameron’s record in government writes Michael Leigh, especially the improvement in the economy, his hard-hitting messages, and the disarray of the opposition. A victory by the opposition Labour Party would have led to Cameron’s replacement as leader of the Conservatives by a more euro-skeptical politician.

Instead, Cameron has received the backing of his party for his election pledge to negotiate a new deal for Britain in the EU, to be followed by an “in/out” referendum to endorse it. The prime minister, the Labour Party, the Scottish National Party, rump Liberal Democrats, and much of British business would argue in favor of continued membership ahead of such a referendum. Opinion polls are showing a ten-point lead for those favorable to continued membership. So at first sight, the prospects for Britain remaining in the EU are good.

However, this scenario is far from certain. Cameron’s demands, including immigration control, the right to limit access to social benefits by foreign workers, , and the repatriation of certain powers to national capitals, will meet stiff resistance from other member states. Central European governments have declared their opposition to any limitation on the free movement of workers. German Chancellor Angela Merkel and French President François Hollande share some of Cameron’s reform goals on immigration, the single market, and labor law but will not pay any price to keep Britain inside the EU.

The greatest threat to Cameron’s strategy and to continued EU membership comes from his own party. Cameron’s tiny House of Commons majority of 12 seats will be whittled down by by-elections, desertions, and deaths. Up to 60 Conservative members of parliament would vote against continued EU membership in a free vote. Their numbers will probably grow. Many Tory MPs and voters want to leave the EU and do not care about renegotiation terms or the possible reaction in Scotland.

If Cameron’s strategy for keeping Britain in the EU is to succeed, he must act on two lessons from the past. First, he should negotiate a reform package quickly, preferably by the end of 2015, before his popularity has eroded. This should be followed by an early referendum, in 2016 not 2017 as announced. Secondly, he should not confront other member states with red lines that they cannot meet. Many of his demands can be accommodated through political deals under existing rules. Any call for treaty change, anathema in countries where this would require perilous referenda, should be put off until after the French and German elections in 2017.

If he bears these lessons in mind, Cameron can probably count on the electorate’s common sense, economic self-interest, and fear of the unknown to deliver a vote for Britain to stay in the EU. Washington should be supportive and should work for early breakthroughs in negotiations for the Transatlantic Trade and Investment Partnership, furnishing another reason for Britain to remain within the EU.

Sir Michael Leigh is a senior fellow with the Transatlantic Academy, an initiative of the German Marshall Fund of the United States in Washington, DC.

– See more at: http://www.gmfus.org/blog/2015/05/18/brexit-views-brussels-berlin-paris-and-warsaw#Party