Do we vote for our own Prime Minister? I certainly didn't.
When did they vote to leave? They voted down the Lisbon/Nice treaties, and then voted for them after re-negotiation of the terms. It's no different to amending bills in the normal democratic procedure.
We voted in the party bassed on its leader among other things, the EU president is a appointed and no one outside the club has a say.
No one got a vote on the Lisbon treaty, France and Holland rejected the constitution so they call it a treaty because no one gets a referendum on treaties. Very under hand and very undemocratic.