It is absurd to claim, as so many people do, that "The electorate do not vote for the Prime Minister." That is true only in that individuals' do not actually put a physical cross against the PM's name on their voting-slips in their local constituencies.
At general elections, there are multitudes of electors who wouldn't even recognise their own MP if he/she came knocking at their front door! What these people do is put their crosses against the name of the person standing locally for the party...and, therefore, leader...they want in power. Do you seriously contend that no one in Dorset ever "voted" for Mrs Thatcher even though she stood in Finchley?
As for those of you who so often refer to Gordon Brown's "inheriting" Number Ten, he was unopposed in the planned election and thus won it 'by acclaim', as it were. This is standard in just about every voting situation in the UK, even for the post of secretary at the local tennis club! In such circumstances, votes are NOT required.