I'm not sure what "database rights" refers to specifically, but the whole matter is actually rather complicated, because the EU copyright directive has a lot of optional exceptions that member states may or may not adopt.

Most of these exceptions only apply to non-commercial use though. So they wouldn't apply in a case like hiQ.

UK specific exceptions are explained here:

https://www.gov.uk/guidance/exceptions-to-copyright

Unfortunately, both Labour and the Tories have taken a relatively hard line in the EU copyright negotiations, so it seems unlikely that things will be relaxed very much after Brexit.

Database rights are a copyright-like intellectual property regime for databases.