Another I just thought of is the fact that any decision taken in Europe will not apply to the UK. It is well established case law (recent decisions and reason by Judge LJ [localgover...wyer.co.uk] repeated from previous decisions such as those of Baroness Hale of Richmond and Sir Nicolas Wall, President of the Family Division of the High Court) that EU Law does not supercede UK domestic Law*.
EU law does not superceede any national law in any country (well, perhaps with very few exceptions which I not aware off).
The EU law system works like this: every new EU law is basically "reference" for wich the participating countries craft a similar national law. For that they usually have a grace period of about 5 years.
And: the UK do the same, they also incorporate EU laws by issuing the relevant national laws.
European regulations work directly in all memberstates (even in the UK). For instance a the regulations on the Common Agricultural Policy work directly in memberstates. This is mostly about paying out European money. Other harmonisation in the EU works with directives, that the memberstates have to implement (and the EU commission has a right to sue memberstates who do not implement). I would presume that the data law is a directive: it would need implementation in the memberstates. Directives can have a direct influence: if a memberstate does not implement and the directive would give citizens a clearly identifiable right, you could use local courts to reach the European court. This has been happening at least since the sixties of the last century...