America has publicly voiced its concern about the consequences of Britain leaving the European Union, stating that London’s “voice” within the EU is “critical to the United States”.

Philip Gordon, the US assistant secretary responsible for European affairs, said that Britain’s membership of the EU was “in the American interest”.

His remarks came as David Cameron prepares to deliver a speech on Europe later this month. The British Prime Minister is expected to promise to renegotiate Britain’s membership and then put the new terms to a referendum. Many Conservatives, including some Cabinet ministers, believe that a ‘No’ vote would mean Britain leaving the EU, although Mr Cameron says he opposes an exit.

Mr Gordon, the senior US diplomat with direct responsibility for relations with the EU and its member states, said that it was for the “British government and the British people to define their relationship with the European Union”.

However, he stressed the importance that Washington attaches to Britain’s current position as a leading member. “Britain has been such a special partner of the United States – that shares our values, shares our interests, has significant resources to bring to the table. More than most others, its voice within the European Union is essential and critical to the United States,” said Mr Gordon.

“There are a lot of inevitably technical and detailed issues that have to be sorted out for every member of the European Union as it moves forward, but as a broad and general theme, we value a strong UK voice in a strong European Union.”

Other US officials have spoken privately about the importance of Britain staying in the club. Last month, one described the EU as a “force multiplier” which was more effective with Britain inside. During an official visit to London, Mr Gordon was the first to make the point in public.

He qualified his analysis by making clear that Britain would keep its “special relationship” with the US regardless of any decision about EU membership. “Britain is an important player in the world and it’s certainly a long-standing and important friend of the United States – and it always will be,” he said.

But Mr Gordon said that America was increasingly dealing with the EU as a whole, rather than any individual member. “We have a growing relationship with the European Union as an institution which has a growing voice in the world – and we want to see a strong British voice in that European Union. That is in the American interest,” he said. “What’s in the British interest is for the British people and the British Government to decide.”

The crisis in the eurozone has led to a wholesale re-evaluation of the EU’s institutions and structures. Mr Cameron’s expected demand for Britain to have new terms for its membership will make the situation more complicated.

Mr Gordon voiced America’s frustration about the prospect of the EU enduring years of internal wrangling. “We welcome an outward looking European Union with Britain in it,” he said.

“We benefit when the EU is unified, speaking with a single voice and focused on our shared interests around the world and in Europe. The more the European Union is focused on its internal debates, the less it’s able to be our unified partner abroad.”

Mr Gordon added: “Every hour at an EU summit spent debating the institutional make-up of the European Union is one less hour spent talking about how we can solve our common challenges of jobs, growth and international peace around the world.”

In response to Mr Gordon, a Downing Street spokesman said: “The US wants an outward looking EU with Britain in it, and so do we.”

On Wednesday, David Cameron told MPs that he would seek to renegotiate Britain’s relationship with the EU before putting the “new settlement” to a referendum of the public. This is expected to happen in about 2018 if Mr Cameron wins a majority at the next election.

The Prime Minister has repeatedly said that he does not support leaving the EU, particularly the single market. However, up to eight Cabinet ministers including Michael Gove, Owen Paterson and Chris Grayling are understood to believe that the Conservatives should now consider leaving.

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