"I am confident that if there is to be a referendum one day, the UK citizens will decide to stay in the EU and contribute to shape its future," he said. "I think the EU does not need unwilling Europeans."

Britain is a net contributor to the European Union and an important player in the single market, which may give Cameron some additional sway -- but critics warn he is taking a big gamble.

Former Belgian Prime Minister Guy Verhofstadt warned against trying "hold the EU to ransom."

Verhofstadt, who leads the Alliance of Liberals and Democrats for Europe in the European Parliament, said Cameron's speech was "filled with inconsistencies" and showed "a degree of ignorance about how the EU works."

"By holding out the prospect of renegotiating the terms of Britain's membership of the EU and subjecting it to a referendum, David Cameron is playing with fire," he said.

U.S. President Barack Obama last week told Cameron that "the United States values a strong UK in a strong European Union."

And Philip Gordon, the U.S. assistant secretary for European affairs, also made it clear that there would be consequences for Britain if it either left the EU or played a lesser role in Brussels.

"We have a growing relationship with the EU as an institution, which has an increasing voice in the world, and we want to see a strong British voice in that EU," he told reporters at the U.S. Embassy in London.

"That is in America's interests. We welcome an outward-looking EU with Britain in it."

Markets across Europe were flat Wednesday morning after Cameron's speech, including in London.