That's a common misconception. Why? In other countries, the civil service aren't the only ones that can propose legislation.
In the EU, the European Parliament can't propose legislation, the European Council can't propose legislation, only the European Commission can propose legislation. You may be electing people to represent you, but how are they meant to represent you when they have no input into what is being discussed? All they can do is say yes or no to what the Commission proposes, it's the Commission that controls the agenda.
Also, it's not a simple "yes/no" ability for the parliament. They certainly can (and do) modify proposed legislation.
A nitpick: The European Council, which appoints the President of the Commission, is composed of the heads of state or heads of government, which depends on the individual member state. E.g., for Britain, the PM (head of government) is a member of the Commission, not the Queen (head of state).
Just wanted to clarify how things work, as many have no idea. And for all its faults, I certainly don't think it's reason enough to leave the EU.
(Personally, as a Swede, I'm very happy to have the CJEU which is the only thing that can stand between Sweden and mass surveillance, as Sweden lacks a constitutional court, as - apparently - our local politicians cannot make bad laws.)