Washington firmly believes that the departure of its strongest partner in Europe would also reduce American influence on the continent, as Britain so often shares American views.
An EU without Britain would be seen as weaker on free trade and less reliable on defence and foreign policy issues.
With British Prime Minister David Cameron saying a Britain out of Europe was now "imaginable", and the prospects of a referendum growing, US agitation has reached a new high.
After observing the increase in popularity of the UK Independence Party and the rise of anti-European sentiment generally, the issue was raised by President Barack Obama in a video conference call with Mr Cameron yesterday.
It was also high on the agenda of a visit by a US national security council official to Downing Street and the Foreign Office earlier this week.
"It is important to state very clearly that a strong UK in a strong Europe is in America's national interest," said a senior US administration official. "We recognise national states but see the EU as a force multiplier."
The White House is perplexed by the view held by some Euro-sceptics that the so-called Special Relationship would be enhanced by a British exit.
It acknowledges that some countries, such as Britain, matter more than others in the EU, dismissing the notion that Washington only wants one telephone number to dial for Europe to make life easier.
Britain's free trade philosophy is regarded as vital in preventing the union from drifting towards protectionism. Since the Second World War, successive British governments have been more assertive on a variety of foreign policy issues, and more in line with American thinking, than other major European nations.
"We understand that a Europe without the UK would be a weaker Europe," said a Whitehall source. "We are getting more and more questions about this, particularly from the US and China. People want to know what it would mean.
"But at the moment we are focused on making Europe work better for us. We are focusing on free trade, the single market and commerce. We are committed to making the EU more competitive."
With the eurozone still in danger of collapse, and momentum building on the continent for greater fiscal and political union, the British government has edged towards holding a referendum on EU membership. (© Daily Telegraph, London)