Membership of the EU also gave the UK access to all manner of databases related to internal security. Until the end of the transition period, the UK has full access to:
Passenger name records
The European Criminal Records Information System (ECRIS)
The Prum database of DNA records
The Secure Information Exchange Network Application
The Schengen Information System (SIS II)
The Schengen Information System, for example, allows participating countries to share alerts on law enforcement in real time. That means when anyone gets checked anywhere, other countries know about it straight away.
Police officers use it on a daily basis to try to trace people with warrants issued against them, defendants or witnesses absconding from court, stolen cars, missing people or those under surveillance.
Richard Martin, deputy assistant commissioner with the Metropolitan Police. told MPs in July that British officials checked SIS II some 603 million times last year, and everyone involved in security agrees that it is incredibly useful.
But under current rules you can only get full access to SIS II if you're in the EU or in the Schengen area (which allows for passport-free travel between most EU member states and some other European countries).
There are other international databases that the UK will be able to use, but Mr Martin said they would not be as quick or effective as the current "at your fingertips" system.
Mr Martin, who heads up Brexit preparation for the National Police Chiefs' Council, also told MPs that using ECRIS takes about six days to get criminal records from other European countries for suspects in the UK. Without such access, he said, it would take 10 times longer.