@Lash,
The Liberal Democrats (here: Nick Clegg) and some from the Labour party claim that the UK will lose access to EU's crime-fighting database after Brexit.
In 2015 the than Home Office minister James Brokenshire (PM May was head of the Home Office in those days) hailed the system as "another vital weapon in the fight against global crime and terrorism".
But since the database is an EU creation governed by the European Court of Justice, no country outside the Schengen zone and the EU has full access. (The USA and Australia have association agreements with Europol, but their police cannot search the database directly.)
This Brexit risk might be solved - similar the participation with Europol and Eurojus, but the legal and political complexities need some compromisses from the UK, and the EU to accept another bureaucracy, namely a new independent arbitration body (which would assess rulings made by the EU court)