Still, despite its sweeping gains in the local British elections, the Independence Party will not control a single local council and does not have a single member in Parliament. Nor does it have a coherent set of economic policies. But Mr. Farage’s message — British values, British beer, controls on immigration from within the European Union and a British exit from the bloc — is clearly resonating with disaffected voters from across the spectrum who are angry about the cost of living, the drop in real income and years of austerity.

A similar message is echoed by other anti-Europe and more far-right parties, including the National Front in France and the Five Star Movement in Italy.

The Independence Party has already proved itself to be an alternative to the status quo, being to the right of the Conservatives but trying to avoid, or repress, the racism of far-right parties like the British National Party. It has touched a nerve with Britons who believe that jobs are being taken away by immigrants from countries like Romania, Bulgaria and Poland who have the right to travel and work freely within the European Union but are willing to work for lower salaries.

The party could deny the established parties an overall majority in the general election a year from now, with Tories especially concerned that the Independence Party will take away enough votes to block their victory in tight election districts.

“UKIP should be extremely pleased with themselves,” said Tim Bale, a professor of politics at Queen Mary University of London. “But they still face this enormous hurdle of the electoral system, which is going to make it very difficult for them to convert even this level of support into parliamentary seats in 2015.”

A YouGov poll published on Friday about voting intentions for the 2015 general election had the Independence Party at 14 percent, with the Conservatives and Labour tied at 34 percent each, and the Liberal Democrats at 9 percent. That could be bad news for Labour, too, which needs to have a larger share now, since polls traditionally narrow closer to Election Day.

Mr. Clegg, who debated Mr. Farage twice and was considered to have been bested, said, “There’s a very strong antipolitics mood around, a restlessness and dissatisfaction with all the main parties.” He said he would not resign as the leader of the Liberal Democrats.