Obama officials say that the UK would probably be excluded from a trade agreement worth billions a year if it leaves the EU

The Obama administration has warned British officials that if the UK leaves Europe it will exclude itself from a US-EU trade and investment partnership potentially worth hundreds of billions of pounds a year, and that it was very unlikely that Washington would make a separate deal with Britain.

The warning comes in the wake of David Cameron's visit to Washington, which was primarily intended as a joint promotion of the Transatlantic Trade and Investment Partnership (TTIP) with Barack Obama, which the prime minister said could bring £10bn a year to the UK alone, but which was overshadowed by a cabinet rebellion back in London.

The threat by Cameron's ministers to back a UK exit in a referendum on the EU raised doubts in Washington on whether Britain would still be part of the deal once it had been negotiated. More immediately, Obama administration officials were concerned that the uncertainty over Britain's future would further complicate what is already a hard sell in Congress, threatening a central pledge in the president's State of the Union address in February.

With formal negotiations expected to start within weeks, the state department already has hundreds of staff working on the partnership. Sources at US-UK meetings in London last week said American officials made it clear that it would take a monumental effort to get TTIP through a suspicious Congress and that "there would very little appetite" in Washington to do it all again with the UK if Britain walked out of Europe.

"Having Britain in the EU … is going to strengthen the possibility that we succeed in a very difficult negotiation, as it involves so many different interests and having Britain as a key player and pushing for this will be important," a senior US official said. "We have expressed our views of Britain's role in the EU and they haven't changed. TTIP negotiations underscore why we think it's important that it continues."

US officials say that the White House is particularly perplexed because Britain played a key role in persuading Obama to stake significant political capital on the ambitious transatlantic partnership. If it is successful it could be the biggest trade and investment deal in history, encompassing half the world's GDP and a third of its trade.

On both sides of the Atlantic there is hope that the boost provided by removing remaining barriers to US-EU trade and investment — worth about $1bn (£660m) and $4bn respectively – would help lift the west, and then the global economy, out of the doldrums. Writing in the US press this year, the British ambassador to Washington, Sir Peter Westmacott, said "a bold and comprehensive deal could be worth 1%-2% in additional GDP on both sides of the Atlantic. Even a 1% bump would translate, at current GDP levels, into an extra $325bn." He added that the UK shared the Obama administration's optimism that it could be completed in less than two years.

Addressing the Senate last week, the US under-secretary of state for economic growth, energy and the environment, Robert Hormats, said the TTIP "is, in many respects, a once-in-a-generation opportunity to reshape our relationship with the European Union". Hormats added it "will enhance our ability to build stronger relationships with emerging economies in Asia and elsewhere around the world".

Both European and American officials involved in preparatory talks on the partnership said that it was also intended as a bulwark against the economic challenge of China, aimed at forming a bloc powerful enough to lay down the rules of international trade and investment.

They pointed to the fact that Turkey's prime minister, Recep Tayyip Erdogan flew to Washington this month specifically to try to persuade Obama to include his country in negotiations. Officials said this was a reflection of the gravitational pull the partnership could exert on the rest of the world.

Gary Hufbauer, a former US Treasury official now a senior fellow at the Peterson Institute for International Economics, said that the administration's hopes to complete a far-reaching partnership in Obama's term may be over-optimistic and would be torpedoed altogether by a British exit from the EU.

"If the UK separates from the EU, I think will go a long way to derail the TTIP project entirely," Hufbauer said. "There would be a lot of questions raised. The administration has many battles ahead of it. It will add another layer of confusion on an already confused picture, and there will be lots of commercial concerns in the US [from those who] have had their eye on the UK markets."

The TTIP will aim to remove the relatively low tariffs of about 3% to 5% between the US and Europe, but its greatest impact will be felt in promoting investment in both directions largely by the convergence of regulations on either side of the Atlantic. One of the greatest potential advantages for the EU would be the opening up of tenders at the US state level to European suppliers. But in return, Europe would have to give up existing protections on its agriculture, film industry and public services.