Retired businessman Christopher Tappin is the latest Briton to fight and lose a long battle against extradition to the US, where he could face 35 years in jail.
Tappin, 65, from Orpington, Kent, denies claims he sold batteries for surface-to-air missiles to Tehran and his is one of a series of high-profile cases which have raised concerns over the fairness of the UK's arrangements with the United States.
Among the first defendants to fight against extradition to the US under the treaty were the NatWest Three.
Bankers Gary Mulgrew, Giles Darby and David Bermingham fought and lost a four-year battle against extradition to the US over allegations of conspiring with former Enron executives to dupe the bank out of 20 million US dollars (£12.7 million).
The men later admitted one charge of wire fraud and were sentenced to 37 months in jail.
But their case prompted an emergency debate in the Commons as MPs and supporters argued that their alleged offences were committed in the UK so they should be tried here instead.
The debate prompted Nick Clegg, then the Liberal Democrat home affairs spokesman but now Deputy Prime Minister, to call for the Government to change the "lopsided" treaty.
The British people do not understand "why there appears to be such an imbalance between the minimal information required to extradite a UK citizen to the US compared to the more substantive justification required to extradite US citizens to the UK", he said.
"This is an issue of overwhelming public interest, yet it has been a real struggle to get the Government to acknowledge the significance of this issue."
High-profile figures still fighting extradition to the US include Gary McKinnon, who faces allegations he hacked into Pentagon computers while searching for evidence of "little green men".
The 46-year-old, from Wood Green, north London, who has Asperger syndrome, faces 60 years behind bars if convicted of hacking into Pentagon and Nasa computers between February 2001 and March 2002.
David Cameron and Mr Clegg have publicly condemned plans to send him to the US, and there has been a long-running campaign for McKinnon to be allowed to remain in the UK following warnings from medical experts that he could kill himself if sent to the US to face trial.
The case is before Home Secretary Theresa May, who will make the final decision as to whether McKinnon should be extradited.
Earlier this month, marking 10 years since McKinnon's first arrest, his mother Janis Sharp said he was "unable to control the terror that consumes his every waking moment" as his extradition battle continues.
The treatment of her son was "barbaric", she said, as she called for Mr Cameron to raise his case with US president Barack Obama when the two leaders meet at the White House next month.
Student Richard O'Dwyer, 23, is also fighting attempts to extradite him to the US over claims he broke American copyright laws.
O'Dwyer, who was arrested in November 2010, allegedly earned more than 230,000 US dollars (about £146,000) through the TVShack website he created, which enabled users to watch films and television shows for free.
His case topped a list of subjects that American voters put to Mr Obama during an online question-and-answer session last month.
O'Dwyer's lawyers have said he would be the first British citizen to be extradited for such an offence and would effectively become a "guinea pig" for copyright law in the US.