Re: And the house of lords?
"The EU laws are decided upon and drawn up by an unelected council. "
Being "unelected" is not a synonym for "lacking democratic legitimacy".
The European commission is appointed by elected governments and approved by the European parliament. So you have two ways to influence it. And this has parallels in both the UK and the US. In the US, the whole "cabinet" is unelected - appointed by the elected head of state. And the British government can appoint ministers by making them members of the House of Lords.
And while, yes, only the Commission can initiate legislation, the European parliament can ask the Commission to draft legislation as, apparently, can we - if we can get a million signatures on a petition. This was decided upon to stop the kind of chaos you see in the US where both houses start bills and then fight over whose bill gets through.