LONDON — British Prime Minister David Cameron travels to Brussels for European Union (EU) budget talks needing to show restive lawmakers in his Conservative Party he can win results abroad that have eluded him at home.

Fresh from a vote on legalizing gay marriage in the House of Commons two days ago in which the majority of his party opposed him many — of them the same people who have put him under pressure on Europe — the prime minister will face further anger from his party if he fails to build on his promise of a new relationship between Britain and the EU.

“Many Tory MPs are going to face a grilling from their local activists this weekend and, as a result, they’re unlikely to be in the best of moods when Mr. Cameron stands up in the Commons to report on how things went in Brussels,” Tim Bale, professor of politics at Queen Mary University London, said in a telephone interview. “He’s likely to come away from the summit at best empty-handed and at worst facing allegations that he’s actually given something away.”

Cameron, who left an EU summit in November saying he’d vetoed a proposed budget package, said last month that, if he wins the 2015 general election, he will begin a renegotiation of Britain’s membership of the 27-nation bloc, seeking to repatriate unspecified powers. He would then hold a referendum on the results by the end of 2017.

Plot Reports

At home, Britain.’s flatlining economy, a consistent lead for the opposition Labour Party in opinion polls, and the hemorrhaging of Tory voters to the U.K. Independence Party over issues such as gay marriage and immigration, have led to reports in newspapers such as the Mail on Sunday of plots to unseat the prime minister among rank-and-file lawmakers.

It was over Europe, a constant fissure in his party since the 1990s, that Cameron suffered his first House of Commons defeat at the hands of his own lawmakers on Oct. 31, as rebels joined with the Labour opposition to demand he push for a real- terms reduction in the EU budget — not just the freeze he’d been seeking.

Of the 50 Conservatives who voted against him on that day, 38 also voted against him on gay marriage, indicating how entrenched the split in his party has become.

The preliminary approval of Cameron’s gay-marriage plans in the Commons came in a so-called free vote, in which lawmakers were able to act according to their consciences, rather than on the instructions of their party leaders.

Even so, it led to vitriolic attacks on Cameron by some Tory members of parliament, who accused him of betraying his party’s core supporters.

Unusual Venom

“What’s unusual is the venom that has accompanied the split,” Philip Cowley, who teaches politics at the University of Nottingham and specializes in parliamentary revolts, said in an interview. “Free votes usually take the poison out of splits; that’s why they’re allowed.”

The prime minister told lawmakers Tuesday that he expects talks on the bloc’s spending plans to be tough.

“These will be extremely difficult negotiations,” Cameron said during his regular question-and-answer session in the House of Commons. “Our aim is the significant cut that I have spoken about” to the European Commission’s plan for spending 973 billion euros ($1.3 trillion) over seven years.

Cameron’s spokesman, Jean-Christophe Gray, said the prime minister is willing to block a deal again if he is not happy with the level of proposed spending cuts.

“Spending needs to be reduced further from the proposals tabled at the November council,” Gray told reporters in London. “If it doesn’t budge, then a deal isn’t going to be doable.”

French President Francois Hollande told the European Parliament on Feb. 5 that Britain should not be allowed to dictate to the rest of Europe and signaled European unease with Cameron’s boasting that he had won a victory for Britain by blocking the budget in November.

“They say it’s difficult or impossible on the United Kingdom’s side, but why should one country decide for 26 others?” Hollande said. “It was possible to strike an agreement at the last European summit. In order to let others say the failure was a victory, we let it happen and now that’s made an agreement more difficult.”