Vital extradition arrangements between the UK and the United States are being threatened by the loss of public confidence among Britons, MPs said.
There is a risk that the lack of confidence, fuelled by concerns over a series of high-profile cases, "will translate into wider disaffection", the Commons Home Affairs Select Committee warned.
It called for an overhaul of the controversial 2003 treaty which governs arrangements, saying judges should decide where cases are heard, an initial test of someone's guilt should be considered, and the treaty's text should be changed to ensure it is balanced.
The report comes as Home Secretary Theresa May considers the results of an independent review by former Court of Appeal judge Sir Scott Baker last year, which found the treaty was both balanced and fair.
"The committee is proposing significant changes to the extradition arrangements between the US and the UK not because we are critical of the American justice system but because we recognise the importance of robust extradition arrangements between our two countries," the report said.
"Such extradition arrangements are now threatened by loss of public confidence in the UK and there is a risk that, with time, that lack of confidence will translate into wider disaffection.
"We believe that the government should act now to restore public faith in the treaty."
The committee's review of extradition proceedings comes as retired businessman and all-Kent Golf Club Union president Christopher Tappin, 65, is being held in jail in New Mexico while he awaits trial on arms dealing charges after being extradited last month.
Student Richard O'Dwyer, 23, of Chesterfield, is also fighting extradition after being accused of breaking American copyright laws by using his computer in the UK.
And Asperger's sufferer Gary McKinnon, 46, from Wood Green, north London, is still waiting to hear whether he will be extradited over charges he hacked into US military computers 10 years ago.
Keith Vaz, the committee's chairman, said: "The treaty is unbalanced, making it easier to extradite a British citizen to the USA than vice versa.
"The cases of Gary McKinnon, Richard O'Dwyer and Christopher Tappin have highlighted public concern that these arrangements are one-sided.
"Prosecutors must be required to produce evidence in support of an extradition request and the accused should have the right to challenge that evidence in court."
"British citizens should also be given the opportunity to face trial in the UK. This would save both time and money."
He went on: "It has now been two and half years since the Prime Minister said the Extradition Act should be reviewed and five months since (Sir) Scott Baker produced his report.
"Evidence to the committee has shown that the current arrangements do not protect the rights of British citizens. The government must remedy this immediately."
However the US Ambassador to the UK, Louis B Susman, strongly defended the treaty in a statement to the committee, saying it was fair, balanced and "promotes the interests of justice in both our countries".
"Our extradition treaty continues to be widely and wrongly condemned by some in Parliament and in sections of the British media," he said.
"The constant use of skewed arguments and wilful distortion of the facts by some to advance their own agendas remains of great concern to the United States."
He added: "It would be wrong to view the extradition treaty through the prism of individual cases where sentiment and emotion can cloud reality and lead to misrepresentation."
Susman also said he put his faith "in the courts - in this country and in my own - to reach the right decisions based on facts, on law, and on evidence".
David Bermingham, who was one of the so-called NatWest Three bankers and gave evidence to the committee, called for the government to "recognise the strength of feeling on the issue and act now to put right what they have long known is wrong with this awful law".
Bermingham, 49, of Goring, south Oxfordshire, was jailed for 37 months over an Enron-related fraud in a deal with US prosecutors in 2008 after losing his fight against extradition.
Michael Caplan QC, who represented former Chilean dictator Augusto Pinochet in his extradition case, added there was "clearly much public and political unease" around the UK's arrangements.
The government should make the changes called for by the MPs "without delay", Mr Caplan, a partner at the law firm Kingsley Napley, said.
Speaking on a visit to the US earlier this month, Prime Minister David Cameron raised the issue of the extradition treaty with President Barack Obama.
"We will be following this up with further talks between our teams," Mr Cameron said.
"I recognise that there are concerns about how it is implemented in practice and that's what our teams will look at."
Shami Chakrabarti, director of civil rights group Liberty, said: "No one should be sent abroad without a basic case tested in a local court and it's time the government loosened the straightjacket around our judges to let more cases be tried at home."
A Home Office spokeswoman said: "We thank the Home Affairs Committee for its report on extradition.
"We will consider the detail of the report and respond shortly."
A US Embassy spokeswoman said: "Our experts will be reviewing and considering that report.
"Ambassador Louis Susman's remarks to the Home Affairs Committee clearly state the government US views about the treaty and our bilateral extradition relationship, and these are included in the report."