To my knowledge EU Regulations are simply laws that overrule local EU countries' laws, so whether it's possible or not for local laws to be more extreme only depends on such laws being at odds with what the Regulation prescribes (but I'm not a lawyer and only looked into that years ago).
From what I've been told how it actually works is that eu law doesn't apply directly to member states, but member states are required to amend their laws to be at least as strict as eu laws on all matters.
There's not a single type of EU laws, there are "regulations" and "directives".
Regulations are complete laws applicable immediately across the EU as they stand, the states are required to amend any conflicting law but the regulations already automatically prevail on any conflicting local law.
Directives instead need to be transposed into local law by each state individually, and can leave many details to the individual implementations.
