I think that you will find that we don't actually vote for a PM in the UK, we vote for a Constituency MP. It's the fact that he was voted as leader of his party which is in government that makes him PM.
If you want to vote for the PM you need to join the party that is in government and hope there is a leadership challenge. even this does not guarantee you will be voting for the PM as it is only tradition that makes the governing party's leader the PM, they could have a party leader and then choose somebody else as PM.