The House of Commons will, on Monday, debate and vote on demands to change the extradition treaty between the UK and US to provide better protection for British citizens.
It will also call for reform of the European Arrest Warrant (EAW) which can see individuals face transfer to other countries on suspicion of the most minor offences.
It is likely Parliament will vote in favour of reform which will put Mr Cameron in a difficult corner, especially as America is opposed to change.
However, earlier this year the Prime Minister seized on a similar MP debate, on prisoner voting rights, to argue with Europe that the will of Parliament cannot be ignored.
It is welcome news for the families of Britons facing extradition, particularly Janis Sharp, the mother of Gary McKinnon, the autism sufferer wanted by American authorities to answer computer hacking charges.
Dominic Raab, the Tory MP who secured the debate, said: “There is a rising groundswell of support for extradition reform.
“It is high time Parliament stood up to defend our citizens from rough justice under the European Arrest Warrant and UK-US treaty.”
The debate on Monday afternoon will centre on a motion that calls on the Government to “pursue amendments” to the UK-US extradition treaty and of the EAW.
The amendments would include rebalancing the level of evidence needed by each country for an extradition, which critics argue is currently biased against Britons.
The US authorities only need to show “reasonable suspicion” that someone is responsible for an offence while Britain must show the equivalent of “probable cause” to bring an American here.
It also includes a call to introduce the so-called “forum” argument that an individual should be tried in the country where most of the suspected crime was committed, a policy that could benefit Mr McKinnon.
An official review of the extradition rules by retired judge Sir Scott Baker concluded last month that the Extradition Act was not biased and did not need reform.
Mr Raab argued for the Commons debate to be held urgently so that the view of Parliament could be heard before the Government formally responds to the Scott Baker report.
The motion already has cross-party backing and the Liberal Democrats and Tory backbenchers are likely to vote in favour of reform.
Earlier this month Nick Clegg broke with Government ranks and ordered a Lib Dem review of extradition amid fears the Conservatives will not reform the act.
Though not binding, a parliamentary vote to reform would be a headache for Mr Cameron.
In February, he seized on a Commons motion that opposed a European ruling that prisoners should get the vote by 234 to 22.
He used it as ammunition in his row over the influence the European Court of Human Rights should have over domestic policy and the view of parliament.
Melanie Riley, a spokeswoman for Friends Extradited, said: “This is a crucial opportunity for Parliament to fix a law with unintended consequences.
“We urge all MPs, particularly those with constituents whose lives have been blighted by the impact of the US/UK Treaty and the European Arrest Warrant, to attend on Monday and demonstrate their support for change.”