The government's EU leaflet: security
9th May 2016
“EU membership means UK police can use law enforcement intelligence from 27 EU countries, and will have access to fingerprint and DNA information.”
For example, the UK has access to the European Criminal Records Information System (ECRIS), which allows EU member countries to exchange information—including fingerprints—contained in their national criminal records databases on the criminal convictions of EU citizens.
The ECRIS currently only applies to EU members.
This is an agreement between EU members but also extends to non-EU members like Norway.
So there is some precedent for information sharing that includes non-EU member states.