Britain won support from Finland and Sweden on Monday for its efforts to reform its relationship with the European Union. But there is also misgiving in the region that the United Kingdom’s push for a looser affiliation with the continent could lead to a two-speed Europe that sees non-euro countries relegated to second-class status.

Alexander Stubb, Finland’s finance minister, said Britain was justified in demanding further liberalization, especially in services, as well as restrictions on welfare benefits for migrant workers.

“Our take is very simple: without the United Kingdom there is no European Union,” he said after consulting with his British counterpart, George Osborne, in Helsinki.

He later told the Financial Times that Osborne’s was a “very constructive approach, results-orientated, problem-solving. It’s a path that will ensure British membership for the foreseeable future,” he said.

The British chancellor, who is seen as a potential successor to David Cameron, has been deputized by the prime minister to lead his country’s negotiations for changes in its European Union membership. Cameron has promised to call a referendum on membership by 2017.

Polls suggest that a majority would vote to stay in the bloc but most Britons also support the ruling Conservative Party’s desire for a less intrusive European Union, one that focuses more on trade and can be checked by national parliaments.

The finance minister of Sweden, which — like Britain — is not in the eurozone, stressed the importance of making sure countries outside the currency union are not neglected.

“For us it is important to have Britain within the European Union and we will of course engage constructively in those discussions that will be coming in that period,” Magdalena Andersson said.

She earlier warned that deeper economic and political integration between countries that use the euro could see the influence of other member states, like Sweden, diminish.

Britain’s reform efforts exacerbate that risk. As the Atlantic Sentinel reported in May, Germany has proposed to link its own push for a more integrated eurozone with the United Kingdom’s desire for a less closer union. This could see Europe end up with an integrated core of euro states surrounded by some loosely affiliated countries like Denmark, Sweden and the United Kingdom.

Britain’s foreign secretary, Philip Hammond, confirmed that such a two-speed Europe was one of his objectives. “We seek reforms that will allow those countries that want to integrate further to do so while respecting the interests of those that do not,” he said in June.

Denmark — the only other member state with a formal opt-out from the euro — earlier said it supported Britain’s proposals. Lars Løkke Rasmussen, the liberal party leader and prime minister, said it would be a “disaster” for Europe if David Cameron was unable to keep Britain in the union.

“Some of the points the British are prioritizing match my own thinking,” Rasmussen said in June, “namely that we need to strike a new balance between the free movement of labor and what welfare services those rights entitle a person to.”