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 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".
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-Qa'ida 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 20 million US dollars.
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".
Measures to allow a judge to refuse extradition where the alleged offence took place wholly or largely in the UK are already in the Police and Criminal Justice Act 2006 and it "is difficult to understand" why they have not yet been put into practice, the MPs and peers said.
The committee added that the "mere presence" of a human rights bar was not enough to secure effective protection for human rights and detailed safeguards should be spelled out.
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, saying "the powers of the judge in an extradition case should instead ensure adequate protection of rights".
It also called for the European Arrest Warrant to be reformed "to correct a number of serious problems".
Measures should be taken to ensure the use of the warrants was proportionate to the alleged crime and that other EU member states do not use them to investigate a crime instead of getting someone to stand trial.
The European Investigation Order should also allow judges to refuse a request on human rights grounds, if the alleged crime is not an offence in the UK, or if the use of such an order would be disproportionate.
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.
"We must not lose sight of the fact that we are dealing with the freedom of individuals: if extradited they are separated from their families, often held in custody in a foreign jurisdiction, alone, many miles from home.
"Extradition itself is a draconian measure that should be reserved for only the most deserving of cases."
He went on: "It would be deeply troubling if we were to subsequently find that a person extradited had lost the opportunity to advance persuasive, perhaps convincing, arguments against their extradition had the recommended changes been implemented."
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".
Sophie Farthing, of the civil rights group Liberty, said: "The current regime takes key decisions out of the hands of British judges - leaving everyone in the UK vulnerable to the injustice of instant extradition.
"Having been so vocal in opposition, we expect the Government to act on these recommendations and reinstate the crucial safeguards so desperately needed."
Catherine Heard, head of policy at Fair Trials International, added the European arrest warrants needed to be reformed to "tackle serious cross-border crime without sacrificing human rights".
A Home Office spokesman said: "The UK's extradition arrangements are currently being reviewed by an independent panel to ensure they operate effectively and in the interests of justice.
"The JCHR's inquiry was conducted to inform this review and the panel will take into account the committee's conclusions. We expect the panel conducting the review to report at the end of the summer."