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Emma Reynolds, the Labor member responsible for European affairs, said, “When unemployment is reaching a 17-year high, inflation is rising and the cost of living is going up, now is not the time to be debating whether to cut off our ties to our largest export market.

“The only real way to reform the EU is to be at the center, working with others to make it better, rather than shouting from the sidelines.”

The vote also exposed differences on EU membership within the Labor ranks. Nineteen Labor members, including euro critic Gisela Stuart, defied Mr. Miliband’s order.

“Apart from defense and a single currency, every aspect of British life has a dimension which has its roots in Brussels,” she said.

“No one under 50 has been asked whether that is what they want. So it’s about time the people are given their voice. If politicians don’t trust the people, why should the people trust their politicians?”

Graham Stringer, a Labor member who voted for the motion, told BBC Radio, “I think it is a mistake of all three party leaders when the public are clearly aching for a say on Europe to say, no, you can’t have it.”

Britain’s relationship with the EU always has been uneasy. Many Britons feel that Brussels has too much power over domestic affairs.

In the most recent opinion poll, carried out for the Guardian newspaper this week, 70 percent of voters want a referendum on British membership in the EU. The survey also found that 49 percent would vote to leave the EU, while 41 percent would vote to remain.

This is not the first time Europe has been a problem for a Conservative leader.

John Major, prime minister from 1990 to 1997, was brought down by euro critics in his party who opposed greater concentration of powers in Brussels.

Disagreements over Europe also eventually helped defeat Margaret Thatcher, prime minister from 1979 to 1990, who rejected proposals that would convert the European Economic Community into the European Union. She was ousted by pro-Europeans in her party.

For Mr. Cameron, the issue is arising as he is comes under pressure over the resignation of his defense secretary, Liam Fox. Mr. Fox quit after revelations that he had allowed a friend to access sensitive information and to attend meetings where government business was discussed.

The prime minister is also in trouble with female voters.

Polls show a decline in support among women after economic austerity measures hit women harder than men.

Many also are questioning his attitude toward women after he made comments perceived as patronizing and sexist in Parliament.

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