MPs have urged the Government to improve safeguards for British citizens wanted by authorities overseas by reforming extradition laws.

The House of Commons agreed without a vote to call on ministers to bring forward new laws and attempt to change the UK-US extradition treaty and European Arrest Warrant regime.

Immigration minister Damian Green told the Commons: "The Government is currently considering what action it will take to ensure that this country's extradition arrangements work both efficiently and fairly."

The motion agreed by the Commons is not binding on the Government, but Mr Green said the views of MPs would be considered as part of the response to the independent review of the UK's extradition arrangements by Sir Scott Baker.

The Commons debate was granted by the Backbench Business Committee to Tory Dominic Raab, who called for ministers to "inject a dose of common sense into the blunt extradition regime".

The UK's extradition treaty with the US has been criticised in relation to a number of high-profile and long-running cases including alleged computer hacker Gary McKinnon and terror suspect Babar Ahmad.

There were also concerns about the European Arrest Warrant, which Mr Raab (Esher and Walton) described as "Kafkaesque", saying: "Fast-track extradition in the EU is based on a leap of faith. It is based on an assumption that all European justice systems are of a decent standard. That assumption is a sham."

Asperger's sufferer Mr McKinnon has claimed he was searching for evidence of "little green men" when he allegedly hacked into Nasa and Pentagon computers from the bedroom of his north London flat. He faces a lengthy jail term if the extradition goes ahead and he is convicted.

Mr Raab said: "Gary McKinnon should not be treated like some gangland mobster or al Qaida mastermind." He told MPs the Commons the motion "is not about abolishing extradition, which is vital to international efforts in relation to law enforcement; it's about whether, in taking the fight to the terrorists and the serious criminals after 9/11, the pendulum swung too far the other way".

Conservative former shadow home secretary David Davis said he believed the arrangements with the US were unfair, with the Americans receiving more suspects from Britain than it extradites to the UK.