MPs are calling for British citizens facing extradition to be given greater rights - equal to the protection afforded to Americans under the UK-US treaty.
The Joint Committee on Human Rights (JCHR) says the Government should renegotiate the UK's extradition agreement with the US.
US authorities should be required to show enough evidence to establish probable cause before a Briton can be extradited, the committee said in a report.
Judges also need the power to refuse extradition requests if the alleged offence took place wholly or largely in the UK, the MPs and peers said.
The report follows a series of high-profile cases, including that of retired businessman Christopher Tappin and alleged computer hacker Gary McKinnon - campaigners have argued it would be best for both men to be tried in the UK.
And now a teenager suspected of masterminding a global computer hacking plot from his bedroom could face a fight against extradition to the US.
Ryan Cleary was arrested at his family home in Essex yesterday as part of a Scotland Yard and FBI probe into LulzSec, a group claiming responsibility for hacking attempts on the UK's Serious Organised Crime Agency, the US Senate and the CIA.
Home Secretary Theresa May has said a review of the UK's extradition arrangements is looking at whether the UK-US treaty is "unbalanced" and a report is expected later this summer.
Critics of the Extradition Act 2003 argue it is unfair for the US to require "sufficient evidence to establish probable cause" before agreeing to extradite anyone to the UK, while Britons are not afforded the same protection.
Dr Hywel Francis, chairman of the JCHR, said the UK's current safeguards were "clearly inadequate" and were failing to protect human rights.
The committee also urged the Government to "urgently renegotiate" the UK-US treaty to ensure extradition requests are refused if "the UK police and prosecution authorities have already made a decision not to charge or prosecute an individual".
It referred to the cases of terror suspect Babar Ahmad and the so-called NatWest Three.
Mr Ahmad, 37, was arrested in the early hours of December 2, 2003, on suspicion of leading a group that provided support for al Qaeda and other fundamentalist networks.
He was never charged in relation to his arrest but has spent nearly seven years in British prisons without trial awaiting extradition to the US for alleged terrorism offences.
And the NatWest Three - 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 $20m.
The men admitted one charge of wire fraud and were sentenced to 37 months in jail.
Judges should play a more active part in extradition cases to ensure their role "is more than only 'rubber stamping' extradition requests", the committee said.
Making countries show there is a case to answer first would reduce the likelihood "that a person could be extradited on speculative charges or for an alleged offence which they could not have committed".
Former home secretary David Blunkett, who signed the Extradition Act, has admitted that he may have "given too much away" to the Americans.
Michael Caplan QC, who represented former Chilean dictator Augusto Pinochet in his extradition case, called for the Home Secretary to defer all contentious decisions until she has considered the JCHR report and the findings of the review.
"Any changes to our extradition procedure should take place without delay," he said.
"Extradition itself is a draconian measure that should be reserved for only the most deserving of cases," he added.