Intelligence experts have clashed over the impact Brexit would have on the UK's safety after a former head of MI6 claimed the cost of a vote to leave would be "low" and could result in "security gains".
Former Secret Intelligence Service chief Sir Richard Dearlove said getting out of the European Union's free movement rules could boost security.
He also suggested that there were "vastly varying levels of professionalism in intelligence and security" across the EU's 28 member states, hinting some of them leaked like "colanders".
But his views were challenged by other former spy chiefs, with former GCHQ boss Sir David Omand saying the "UK would be the loser in security terms from Brexit, not the gainer".
Rob Wainwright, director of Europol, insisted Britain had "come to rely" on access to EU crime and intelligence databases.
Europol is "concerned" Islamic State (IS) has a "more widespread network than we first feared", which is behind the "new unprecedented threats that we face", he added.
Mr Wainwright said it was important that intelligence networks across Europe should "come together" in the fight against IS but added that there had been "huge" progress in co-operation across the EU.
"I certainly respect Sir Richard's views but in the 10 years or so since he left office I have seen huge progress in the EU in building up a far stronger capability to fight terrorism and serious crime," he added.
"The UK has very often been the driver of that work."
Last year 2,500 new cases of cross-border crime and terrorism were launched through Europol by the British authorities, he told the programme.
"I see the benefit of that for British police authorities every day," he added.
Writing in Prospect magazine Sir Richard said: "Whether one is an enthusiastic European or not, the truth about Brexit from a national security perspective is that the cost to Britain would be low.
"Brexit would bring two potentially important security gains: the ability to dump the European Convention on Human Rights - remember the difficulty of extraditing the extremist Abu Hamza of the Finsbury Park Mosque - and, more importantly, greater control over immigration from the European Union."
The European Convention on Human Rights is not an EU creation, instead it covers the Council of Europe members.
Sir Richard said "few would notice" the loss of the European Arrest Warrant, which has been highlighted as an important factor by the Remain camp.
"Britain is Europe's leader in intelligence and security matters and gives much more than it gets in return," he said. "It is difficult to imagine any of the other EU members ending the relationships they already enjoy with the UK.
"Furthermore, counter-terrorist and counter-espionage liaison between democratic allies is driven as much by moral considerations as by political ones."
If a German intelligence agency learned of a plot targeting London it "is certainly not going to withhold the intelligence from MI5 simply because the UK is not an EU member".
The former "C" added that the current European intelligence and security bodies were "of little consequence" and "are generally speaking little more than forums for the exchange of analysis and views".
"With the exception of Europol, these bodies have no operational capacity and with 28 members of vastly varying levels of professionalism in intelligence and security, the convoy must accommodate the slowest and leakiest of the ships of state," he said.
"The larger powers cannot put their best intelligence material into such colanders."
But Sir David, the former head of the British eavesdropping agency, said: "That we are the leading provider of intelligence to the rest of Europe is true - but irrelevant to the decision.
"What matters is the value that our relationship to our European partners does bring to our security, especially information to help the management of our border - control of which has always remained in our hands. We need information and assistance from partner countries to help us.
"We are part of an established information sharing network with our partners whilst still retaining control of our border. The best of both worlds. Why jeopardise the flows of information we receive?
"Talk of withdrawal from the European Convention on Human Rights is unreal - unless we are also going to abandon our commitment to the 1948 UN Universal Declaration of Human Rights that we helped draft after the Second World War, on which the European convention is based, and make ourselves an international pariah."
Former shadow home secretary David Davis said EU police and security agencies would continue to cooperate with Britain if it quits the bloc because it has the biggest intelligence databases.
He told Today: "They are really going to not deal with us? This is just a ridiculous argument."
Mr Davis also claimed the jihadists would be able to enter the EU under the new visa deal struck between Brussels and Turkey.
"If you imagine Syrian jihadists can't get Turkish papers then I think you need to look at the politics of Turkey, which means we have opened up, not closed down, access for terrorists."