The UK will lose the automatic power to extradite criminals from some EU states next year even if a Brexit deal is agreed, Theresa May is warned today.

The European Arrest Warrant (EAW) will be undermined by a little-noticed clause allowing countries to refuse to surrender their own citizens, a House of Lords inquiry has found – even during the transition period.

The threat is revealed as the prime minister is warned it will “cost lives” unless she drops her red line to end the jurisdiction of the European Court of Justice (ECJ) in the UK after Brexit.

That refusal risks close integration with Europol, the EU’s law enforcement agency, and access to criminal databases, as well as the extradition powers of the EAW, peers say.

“Red lines won’t save people’s lives – getting agreement on effective police and security cooperation will,” said Lord Jay of Ewelme, the chairman of the Lords home affairs sub-committee.

The committee pointed out that, by mid-May, the Brexit talks had spent “little more than an hour discussing the future internal security relationship” – despite the prime minister insisting it was a priority.

“Neither side, however, has yet approached the negotiations in this spirit,” the report adds.

“The UK Government’s ‘red lines’, and the EU’s response, appear to have narrowed the scope for agreement. While we do not underestimate the difficulty of the issues facing both sides, the current mindset urgently needs to change.”

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Ms May has called for a “deep and special partnership” with the EU after Brexit, in the form of a new treaty to “preserve” the current security cooperation.

But Lord Jay added: “The committee believes it is unlikely that such a treaty can be agreed in the time available.”

The UK government has described staying part of the EAW as “crucial” to prevent a return to “complex, lengthy and often frustrating old-fashioned processes”.

About 2,000 people a year are surrendered from the UK to the EU - and between 200 to 300 handed over to the UK by other EU countries.

However, Article 168 of the draft withdrawal agreement, struck in March, would “authorise EU27 States to refuse to extradite their nationals to the UK during the transition period”.

The committee was told that Germany, France, the Czech Republic, Romania, Slovenia, and Slovakia were most likely to invoke the clause during the transition period, due to run until the end of 2020.

It urged the government to “publish a contingency plan” to prepare for the possibility of not being able to secure an extradition.

The terms of the planned transition will also bar the UK from a governance role in Europol or data-sharing, making it “more difficult to secure long-term access”.

Long-term, the UK also risks crashing out of the Passenger Name Record Directive (information collection by air carriers), Prüm (sharing of DNA profiles, fingerprints and vehicle registrations), the Schengen Information System (alerts on suspected criminals – used 539m times by the UK in in 2017 alone) and the European Criminal Records Information System (information exchange on criminal convictions).

Lord Jay added: “The Government wants an overarching security treaty, which would to a large extent replicate the status quo. We don’t think this is achievable in the time available.