DAVOS, Switzerland — British Prime Minister David Cameron wants nothing to do with a United States of Europe, an idea that’s gaining currency as the countries that use the euro struggle to fix their debt crisis.

A day after he shook up Europe’s political landscape by offering citizens the prospect of a vote on whether to stay in the 27-country European Union, Cameron insisted Thursday he wants Britain to remain an integral part of the bloc but that more unification would not be the answer.