Britain’s June 23 referendum — in which immigration was a central issue — was the first time a country had decided to quit the European Union, and it bolstered euroskeptic parties across the Continent, including in France, the Netherlands, Germany and Italy.

After the British vote, Mr. Hofer said he favored holding a similar referendum in Austria if new efforts to centralize power in Brussels were not halted. On Sunday, he told the newspaper Österreich that if the European Union “evolves in the wrong direction, then for me the time would have come to say: So, now we have to ask the Austrians.”

In a 1994 referendum in Austria, 67 percent of voters chose to join the European Union, and recent polls suggest that a clear majority supports continued membership, said Mr. Rauscher, the newspaper columnist.

Any new referendum would have to be approved by Parliament, but the Freedom Party could begin a grass-roots appeal for a referendum like the one in Britain. “Parliament could ignore that,” Mr. Rauscher wrote in an email, “but that would be a good propaganda tool for the Freedom Party.”

The decision by British voters to leave the European Union was strongly influenced by immigration from other European countries, but Britain, which is not part of the Schengen visa-free zone, has not felt the crush of Middle Eastern and North African refugees in the same way that other European nations have. Slovakia and other smaller countries have objected to the quota plan devised by European leaders. Germany has insisted that all members of the bloc must do their share to solve what is a common problem.

But the British vote and the sparks it has ignited among other European electorates are now exerting intense pressure on Chancellor Angela Merkel of Germany and others who favor cautious and collaborative institutional reforms. That stance is arousing increasing resistance from states, and political parties, that want to chart their own path.