US President Barack Obama said on Friday that Britain would not be able to strike a free trade deal with the US "any time soon" if it leaves the EU, as Washington's focus would be on reaching agreement with the European Union, The Daily Mail reported.

The President was speaking after Downing Street talks with Prime Minister David Cameron during a two-day visit which he has used to speak out in favor of continued UK membership of the 28-nation bloc after the June 23 referendum.

At a joint press conference in the Foreign Office, Cameron insisted that the special relationship between the UK and US was not "constrained" by Britain's EU membership.

Obama said the UK would be "in the back of the queue" for a trade deal if it left the EU, because the US would focus on the bigger bloc.

The US president stressed that the referendum was a "decision for the people of the United Kingdom" and he was "not coming here to fix any votes".

But he defended his right to offer an opinion, saying: "In democracies everybody should want more information, not less, and you shouldn't be afraid to hear an argument being made - that's not a threat, that should enhance the debate.

"Particularly because my understanding is that some of the folks on the other side have been ascribing to the United States certain actions we will take if the UK does leave the EU - they say for example that 'we will just cut our own trade deals with the United States'.

"So they are voicing an opinion about what the United States is going to do, I figured you might want to hear from the president of the United States what I think the United States is going to do.

"And on that matter, for example, I think it's fair to say that maybe some point down the line there might be a UK-US trade agreement, but it's not going to happen any time soon because our focus is in negotiating with a big bloc, the European Union, to get a trade agreement done.

"The UK is going to be in the back of the queue."

Trying to do "piecemeal trade agreements" was "hugely inefficient", he said.

Setting out the choice facing the UK, the president said: "If, right now, I have got access to a massive market where I sell 44% of my exports and now I'm thinking about leaving the organization that gives me access to that market and that is responsible for millions of jobs in my country and responsible for an enormous amount of commerce and upon which a lot of businesses depend - that's not something I would probably do."

He added that the UK's membership of the EU "enhances the special relationship" because it meant Washington had a trusted partner in Europe on issues including the fight against terrorism.

"Precisely because I have a confidence in the UK, and I know that if we are not working effectively with Paris or Brussels then those attacks are going to migrate to the United States and to London, I want one of my strongest partners in that conversation.

"So it enhances the special relationship, it does not diminish it."

Obama said that while the vote was a matter for the British people, the US had a "deep interest" in the outcome.

"The United States wants a strong United Kingdom as a partner and the United Kingdom is at its best when it is helping to lead a strong Europe," he said.

"It leverages UK power to be part of the European Union. I don't believe the EU moderates British influence in the world, it magnifies it."

He acknowledged that all countries were concerned about their sovereignty, but said that the UK's membership of the EU added to collective prosperity and security.

"All of us cherish our sovereignty - our country is pretty vocal about that - but the US also recognizes that we strengthen our security through our membership of NATO, we strengthen our prosperity through organizations like the G7 and the G20.

"I believe the UK strengthens both our collective security and prosperity through the EU."