Earlier quoted context omitted.
EU law doesn't work like that. Each country has to pass their own local law to enforce the GDPR. For the UK that was the Data Protection Bill 2017.
From wikipedia: The GDPR replaces the 1995 Data Protection Directive.[4] Because the GDPR is a regulation, not a directive, it does not require national governments to pass any enabling legislation and is directly binding and applicable.[5] So, no local laws. It's a regulation.
To say that local courts and laws will have no influence is complete rubbish.