The home secretary also comes under fire for keeping the details of the agreement reached with Washington under wraps when it was announced as a breakthrough last month.
The deal will give police and intelligence agencies speedy access to electronic communications sent by terrorists, serious crime gangs and white-collar criminals.
But the investigation, by a House of Lords committee, has poured scorn on a claim that the UK will be able to contain “credible assurances” that extradited suspects will not be put to death.
It also strongly criticises the “asymmetric” nature of the arrangement – which will give the US far greater powers to target UK citizens than vice-versa.
Robin Hodgson, a Conservative peer and former MP, told The Independent: “What does that mean? What is a credible assurance?
“Where there is separation of powers, how does a politician give a credible assurance that a court will not impose the death penalty, or – if it does impose it – carry it out?
“As a result of this agreement, someone could be sent to the US, sentenced to death and live on death row forever – or put to death, unless that credible assurance works.”
Lord Hodgson, who chairs the Lords’ Secondary Legislation Scrutiny Committee, also pointed to the vastly different powers the agreement will hand to London and Washington.
The UK would only be allowed to obtain data on its own citizens – while the US would be able to demand it from a UK citizen travelling abroad, or an EU citizen living in the UK but abroad.
“We are making it clear that that the next parliament should ask ministers to explain that asymmetry and that extraordinary wording about obtaining credible assurances,” Lord Hodgson added.
The committee’s report, published as parliament was dissolved for the general election, also criticised the “alarming” risk of the handover of data leading to a UK citizen’s transfer to Guantanamo Bay.
The notorious US camp, on the island of Cuba, remains open with around 40 prisoners, despite international condemnation of the indefinite detention and torture of terror suspects.
In evidence to the peers, the Home Office argued the risk of a UK citizen being extradited and sent to Guantanamo Bay was “very limited” but “theoretically possible”.
But their report concluded: “While these assurances are helpful, given the gravity of the matter, we take the view that even a theoretical possibility is alarming.”
The controversy comes after strong criticism of Sajid Javid, the then-home secretary, for paving the way for two notorious British Isis fighters to be sent to the US, despite the risk of execution.
Alexanda Kotey and El Shafee Elsheikh, from the so-called “Beatles” cell, were transferred from detention in Syria into US custody in Iraq last month and are expected to be flown to the US to face the death penalty.
Now the new data-sharing agreement is poised to trigger more such cases by replacing the current, cumbersome “mutual legal assistance” treaty with fast-track arrangements.
It currently takes police and security services between six months and two years to request and obtain electronic data, the government says.
The new deal will compel Facebook, Google and Twitter to hand over the content of emails, texts and direct messages – and require the same of UK companies holding information sought by US investigators.
Ms Patel last month hailed the historic agreement as the way to “dramatically speed up investigations, allowing our law enforcement agencies to protect the public”.
However, it had not approved by parliament before dissolution, ensuring it will be a controversy when the new crop of MPs gathers after the election on 12 December.
The Home Office declined to respond to the criticisms, but pointed out the US would not be permitted to target people while they were in the UK.
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