The Government should renegotiate the UK's extradition treaty with the United States to ensure British citizens get the same protection as Americans, a report has found.
US authorities should have to show enough evidence to establish probable cause before a Briton can be extradited, the Joint Committee on Human Rights (JCHR) said.
Judges should also have the power to refuse extradition requests if the alleged offence took place wholly or largely in the UK, the MPs and peers said.
The committee's report follows a series of high-profile cases, including that of retired businessman Christopher Tappin and alleged computer hacker Gary McKinnon, in which campaigners have argued it would be best for the defendants to be tried in the UK.
Home Secretary Theresa May has said a review of the UK's extradition arrangements was considering whether the UK-US treaty is "unbalanced" and a report is expected later this summer.
Critics of the Extradition Act 2003 argue that 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".
The JCHR report on the human rights implications of the UK's extradition policy found the Home Secretary's discretion to intervene in cases should not be extended. 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.
Mr Caplan, an extradition partner at Kingsley Napley LLP, added that the recommendation for judges to be able to bar extradition if the alleged crimes occurred in the UK was "long overdue". But he said the call for all states to provide robust evidence before applying for extradition "will unfortunately not happen".