Britain recommitted itself to robust participation in Nato, the security alliance that includes most EU members. And British MPs have sought to adapt EU rules so that they could largely preserve the status quo in many security discussions.
But many European leaders - including the chief EU Brexit negotiator, Michel Barnier - say Britain cannot simply pretend Brexit did not happen in the realm of security, and that leaving the club means losing its benefits, even if the other club members lose out, too.
"If you leave this ecosystem, you lose the benefits of this cooperation. You are a third country because you have decided to be so. And you need to build a new relationship," Barnier said.
Although the consequences of Brexit will ripple throughout Britain's security relationships, they will probably be felt most directly in law enforcement and counterterrorism cooperation.
Right now, police and counterterrorism officials can tap into EU databases to check on the people they encounter at border crossings and during traffic stops.
European security officials credit that information sharing, which increased significantly after a spate of terrorist attacks in 2015, with helping to foil major new plots.
British law enforcement officials consulted one crime-stopping database, the Schengen Information System, 539 million times in 2017.
British leaders say they want to keep the current setup in place even after they depart. But EU law enforcement agencies say that while they want to cooperate, they would risk violating their own laws if they shared as much information with a non-member as they do with a member.
Large portions of data about EU citizens are okayed for sharing only with other EU members, in part because the EU has a common set of rules about privacy and what can be done with the information.
Once London has pulled out of the common regimes, EU law enforcement officials expect their databases will have to be scrubbed of British contributions, and vice versa.
Britain is likely to have to request information from the databases on a case-by-case basis - a far cry from having immediate and direct access in every patrol car.
And what the EU may be willing to share may become more limited over time.
Britain wants to leave the EU to gain more sovereignty over its own policies - making Europeans fear that it could soon go in a different direction on data rules.
Moreover, as technology evolves, it will force new decisions about how to balance civil liberties and safety. There is the potential for the two former partners to grow further and further apart.
"The basic intention of both sides, the EU and the UK, is to get along as well as possible after the divorce for the benefit of the children," Dutch Foreign Minister Stef Blok said. "But certainly Brexit will complicate things."
Brexit is also likely to deal a blow to European unity on international affairs.
Britain - a nuclear power and a permanent member of the UN Security Council - has long held outsize influence in determining Europe's role in the world. British diplomats brag that they are responsible for about two-thirds of the work in shaping EU sanctions policy.
Britain probably will remain a sanctions hawk. But its officials will be outside the room when EU sanctions decisions get made. That means the EU may in some cases end up taking a softer line. And sanctions regimes may be less effective without Britain and the EU in lockstep.
"We have to up our game, we who stay in the EU," said a European diplomat who works on security issues. The British "have been one of the driving forces on the EU sanctions".
London will try to keep up with EU discussions by installing more diplomats with sanctions experience in its embassies in Berlin, Paris and Brussels. But its lobbying may have limited impact. Already, Britain has become an afterthought in sanctions discussions, some diplomats say.
"We simply think that sanctions are necessary, and we will miss the UK," Polish Foreign Minister Jacek Czaputowicz said in an interview. "Because of this, there are less countries who are opposed to Russian policy."
May's Government has warned that cooperation would be compromised further if Britain leaves without any Brexit deal in place - an outcome that has become more likely as March 29 nears and the Prime Minister's version of Brexit remains widely unpopular.
"We and Europe know, from bitter experience, that often when there is a mistake or when something has been missed that we find, time and time again, that it has been due to a failure of cooperation," British Security Minister Ben Wallace told a security convention last month. "A no-deal situation would have a real impact on our ability to work with our European partners to protect the public."
Even an operation as low-tech and basic as an extradition request would be far harder than it is now, with rules snapping back to a 1957 treaty. Many EU countries forbid sending their own citizens to countries outside the bloc to face justice.
In a no-deal Brexit, Britain could also lose the continued access it has negotiated to European plane travel records and databases of vehicle registrations, fingerprints and DNA profiles.
"The impact of the UK leaving is considerable if not managed," Rob Wainwright, a British former director of Europol, the pan-EU policing agency, told a British parliamentary committee. "Literally, people's lives depend on it."
And although British military spending has been rising since the 2016 Brexit vote, any economic hit from the departure would leave less for tanks and soldiers.
The best measure of Brexit's impact on security may be the assessment of Europe's adversaries. Sensing opportunity, they are encouraging as hard a split as possible.
May "must implement the will of the people as expressed in the referendum, or that is no referendum at all," Russian President Vladimir Putin said in a year-end news conference. He mentioned proposals to hold a second referendum to reconfirm British desires to split from the European Union.
"Is this democracy?" he asked.
