From sharing intelligence after terror attacks to pursuing cross-border criminals, security is a potential bargaining chip for Britain in the Brexit negotiations -- but one that must be played carefully, analysts say.

Prime Minister Theresa May warned the European Union on Wednesday that failing to reach a new trade deal once Britain leaves the bloc could damage cooperation against crime and terrorism.

The government denied it was a threat, saying it was simply fact that unless Britain agreed to continue its security cooperation projects, including with law enforcement agency Europol, then it would leave them after Brexit.

Charles Grant, director of the Centre for European Reform, said that in the tough talks ahead with the EU, "Britain's strongest card is its contribution to European security".

Malcolm Chalmers, of the RUSI military think tank, made a similar point -- although he warned against playing it too strongly.

"The temptation to use the UK's 'security surplus' -- its role as the leading West European military and intelligence power -- as a bargaining chip should be resisted," he said in a January briefing paper.

"The UK's contributions to European security can, however, help to remind other EU states of the strong interests and values that they will continue to have in common."

Anand Menon, professor of European studies at King's College London, said on Thursday that May's tone suggested she was trying to play to the eurosceptic press.

"There was a positive way of doing this... of saying exactly the same thing in a way that makes us sound like we're all pointing in the same direction," he said.

British opposition politicians seized on the suggestion that May was playing politics with security -- just one week after an attack on parliament that left four people dead.

"National security too important to use as bargaining chip in Brexit trade negotiations. PM's threat is dangerous," tweeted Yvette Cooper, the Labour chairwoman of the House of Commons' home affairs committee.

Her warning was echoed by the European Parliament's chief Brexit negotiator, Guy Verhofstadt, who said that "citizens' security was far too serious a subject".

'Make Britain less safe'

May stressed she wanted to negotiate continued access to information sharing schemes in the EU -- and she herself has previously warned that reducing cooperation would make Britain less safe.

As well as Europol, Britain makes use of the European Arrest Warrant (EAW), which speeds up extradition requests, and the Passenger Name Directive, which allows potential criminals to be tracked on flights across the continent.

In 2015, Britain also joined the Schengen Information System (SIS II), an EU-wide database of real-time alerts which is particularly useful in tracking suspected foreign fighters returning from Syria and Iraq.

"These are practical measures that promote effective cooperation between different European law enforcement organisations, and if we were not part of them Britain would be less safe," May said last year, when she was still interior minister.

London received 48,766 requests through the EAW between 2010 and 2015, according to the National Crime Agency, while it was used 1,424 times by Britain.

One of those was Hussain Osman, who was arrested in Italy in 2005 after trying to stage a repeat of the London suicide bombings in July that year, which left 52 people dead.

Britain's current interior minister, Amber Rudd, said Britain was the top contributor to Europol and "if we left Europol, then we would take our information... with us".

But the agency's British director, Rob Wainwright, warned last year that if it left, Britain would become a "second-tier member" without direct access to data.

'NATO capability'

Brexit will not affect the way Britain shares intelligence in the "Five Eyes" partnership -- the United States, Britain, Canada, Australia and New Zealand -- nor its leading role in the US-led NATO military alliance.

But Professor Iain Begg, research fellow at the London School of Economics, said that NATO membership in particular could be used as leverage with some of the smaller EU states.

"Security is also the hard security of NATO, where one of the bargaining chips UK does have to play is its NATO capability," he told AFP.

Britain is in the process of deploying 800 troops to Estonia, and also has 150 in Poland to reassure them in the face of Russian aggression.

"That's where Britain can say to a country like Estonia, you back us on some of the things we're demanding in the (EU) exit negotiations and we'll be much more accommodating to you about pushing NATO to locate troops on the Estonian-Russian border," Begg said.