More Britons facing extradition to the USA could be tried in UK courts, after David Cameron and Barack Obama agreed to review the operation of a controversial treaty.

The development could cheer the family of computer hacker Gary McKinnon, who is fighting extradition to the US, but comes too late for Kent businessman Christopher Tappin, who was sent to Texas last month.

The issue of extradition was raised by the Prime Minister with Mr Obama during his visit to Washington. It is understood that Mr Cameron did not mention any individual cases with the US president during their talks.

Mr Cameron is thought to want to explore the possibility of whether more cases can be heard before UK courts, though there are no immediate proposals for treaty changes. Home Secretary Theresa May is considering the Government's response to last year's Scott Baker Review, which found no imbalance between the way US and UK citizens are affected by the treaty.

Mr Tappin's supporters claim he was the victim of entrapment by US agents when he offered to supply batteries for export to Iran that could allegedly be used in surface-to-air missiles. He denies wrongdoing, but has been denied release from custody in Texas.

Mr McKinnon, who suffers from Asperger's syndrome, is facing extradition for hacking US military computers. He claims he was looking for evidence of UFO sightings and is pleading to be tried in the UK.

Mr Cameron said he recognised public concerns about the treaty operates. "I raised this issue with President Obama today and we had a good discussion. We will be following this up with further talks between our teams.

"We have carried out an independent review of the treaty which found that it was balanced, but I recognise there are concerns about how it's implemented in practice and that's what our teams will look at."

The development emerged one the final day of Mr Cameron's three-day trip to the US with wife Samantha. The Prime Minister will travel to New York City to make an emotional visit to pay his respects at Ground Zero. The visit will revive memories of the September 11 2001 attacks on the twin towers for the Camerons, as Samantha was in New York on that day.

The couple were also guests of honour at a lavish state dinner in a marquee on the South Lawn of the White House.