BRUSSELS—U.K. Foreign Secretary Philip Hammond met with European officials on Tuesday, as the British government intensified efforts to try to secure concessions regarding its relationship with the European Union.

British Prime Minister David Cameron, under pressure from some in his party who want to repatriate powers to London or even leave the EU, has promised to secure reforms and then allow the British public to vote on whether to leave the 28-member bloc. Mr. Cameron has said he would argue the U.K. should remain in the EU.

The referendum could be called as early as next year. Though at a news conference on Tuesday evening, Mr. Hammond said negotiations with other EU governments could drag on for another year, pushing the referendum into 2017. “If the negotiation stretches on through the summer [of 2016] and into the autumn, [the referendum] will move into 2017,” Mr. Hammond said. “It’s just too early to say.”

The process is expected to move slowly. “Serious negotiations” over possible concessions for Britain are only likely to begin after a summit meeting of EU leaders in December, Mr. Hammond said. In particular, no progress is likely to be made until after Poland’s parliamentary elections, scheduled for Oct. 25, he said.

During meetings at the European Commission and European Parliament on Tuesday and Wednesday, Mr. Hammond said, he would focus on the four areas the U.K. government has identified as wanting reform, including competitiveness, sovereignty, economic governance and access to welfare benefits by other EU citizens. Among other officials he is scheduled to meet are EU foreign policy chief Federica Mogherini and Martin Schulz, president of the European Parliament.

Mr. Hammond confirmed that Britain will seek changes to the EU’s treaties as part of its reform proposals, a step viewed with deep suspicion in other EU capitals. He said the British government has so far been “exploring the appetite and attitude of different interlocutors, not setting out hard and fast demands.”

Ahead of the visit to Brussels, Mr. Hammond had sounded an optimistic note. “We are confident that we will be able to negotiate a package that addresses the concerns of the British people—but the decision will be for them alone to take in the referendum we have promised,” he said on Monday.

The U.K.’s push comes as Europe is struggling to cope with the biggest wave of immigration since World War II as people are flowing to the continent from war-torn areas like Syria. The U.K. has been accused by some other European countries for not doing enough to help with the crisis.

That could potentially complicate Britain’s efforts to secure concessions if other European countries don’t feel it is doing its part.

Mr. Hammond, though, suggested concerns of some Eastern European governments around large-scale migration from outside the EU could potentially play to Britain’s advantage in the discussions about EU reforms.

“Some of the countries who have the most robust views on [the EU’s] external migration agenda have been the ones with very strong views on no freedom of movement internally,” Mr. Hammond said. “Possibly the challenge of migration is focusing attention on the challenges that [large-scale] migration creates.”

Britain’s effort to push for reforms for the EU is being led by Mr. Cameron and is being conducted in conjunction with Mr. Hammond and U.K. Treasury chief George Osborne.

Mr. Cameron on Tuesday had dinner with French President François Hollande at the British prime minister’s country residence, Chequers, where they were to discuss Britain’s renegotiation efforts and Europe’s migration crisis. Mr. Hollande has said changing EU treaties isn’t a priority and Europe shouldn’t change to suit one country.

In recent days, Mr. Cameron met with Polish President Andrzej Duda, Cypriot President Nicos Anastasiades and Danish Prime Minister Lars Løkke Rasmussen. Those meetings follows those earlier this month with his counterparts in Lisbon and Madrid.

In Brussels, officials are hammering out the technical details of any agreement, a process that began in July and is expected to take several months. Leaders will return to the issue at the EU summit in December.

Some analysts say recent events, including the migration crisis, have added to uncertainty about the outcome of the U.K. referendum. But analysts generally still expect the most likely outcome is for Britain to remain in.

A poll by YouGov PLC published on Tuesday found 44% of people canvassed said they would definitely or probably vote for the U.K. to stay in the EU, while 34% said they would definitely or probably vote to leave. The rest didn’t know or didn’t have a strong preference either way.