Correct me if I'm wrong, but you could vote for MEP as well. And your country was represented by your PM and cabinet as well, which you do elect. QSure, the British MEPs may be overruled by others, but that's also the case for your local MP right?

Though I do think there's a lot of room for improvement in transparency on how the EU operates, and how it is reported. But that your own MPs are 'hiding' by blaming the EU is, frankly, a problem of your MPs that you elect yourself.

Anyway, this is what you guys wanted, so good luck.