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.
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.
