Prime Minister David Cameron could either be remembered as the man who led Britain out of the European Union or the person who managed to keep it in the union.

Cameron believes history will see him as the prime minister who helped "reform" the European Union, he said in an interview with CNN's Christiane Amanpour on Thursday.

"I feel very confident and positive that having set out a plan, having explained to the world ... everyone can see there is a plan to change Europe for the better and to secure Britain's place in it."

In a speech in London on Wednesday, he called for renegotiating the terms of Britain's European Union membership and said that if his party wins the next election, there will be a vote on the membership.

There has been considerable backlash to Cameron's speech from European leaders, as well as from former British Prime Minister Tony Blair, who likened it to the movie "Blazing Saddles," in which a character holds a gun to his head and threatens to shoot himself if he does not get his way.

"To those who disagree, I would just say you cannot attack a plan if you've got nothing to attack it with," Cameron told Amanpour.

Despite sending shock waves across Europe with his speech, Cameron said he had no regrets about the proposal.

"We've set out a plan for how we get change in Europe that will benefit all of Europe, making it more open, more competitive, more flexible, and how we secure Britain's place within that," he said.

Critics see Cameron's move as a gamble, particularly the referendum that could see the UK exit the EU, even if that is not Cameron's goal.

"I think the referendum is vital, because in the end, we should have the consent of the people for what we do," he told Amanpour. "I believe we'll secure the changes that we need and I will be able to recommend to the British people that we vote to stay in the European Union."

Cameron said the biggest risk is not Britain leaving the European Union, but rather the economic hazard if the EU does not pursue reforms.

"The greatest gamble for Britain would be to sit back and do nothing," he said.

Cameron reiterated his belief that the European Union over-regulates in many areas, but he said he will not put a list of demands on tables and storm off if he does not get them.

"What we're saying is that we should, in Europe, we should have changes that will benefit all of the countries of the European Union, but which at the same time will -- I think -- make Britain more comfortable with her place in the European Union."

Not everything that Cameron had to say about the European Union was negative.

"Clearly, there are important benefits from belonging to a single market, the freedom to travel and to live in different parts of Europe," he said. But he stressed that too much regulation was put on the UK, on everything from banking to limits on the hours that doctors can work.

"I think Britain would be better off in a reformed European Union, but I think the right approach is to seek that reform and then hold that referendum."

Key British allies are also concerned, not just about the economic ramifications, but also about the foreign policy implications of a British exit from the EU.

A White House spokesman said that during the Algerian hostage crisis, Obama said to Cameron: "The United States values a strong UK in a strong European Union, which makes critical contributions to peace, prosperity and security in Europe and around the world."

Cameron acknowledged the important role the United Kingdom plays in foreign affairs, signaling that as one of the reasons why Britain is so crucial to the European Union.