Britain hasn't yet decided to directly elect its Prime Minister. But we are about to see the first Prime Minister chosen by a larger section of the public.
Party leaders were traditionally chosen by members of the parliamentary party. It's amazing to think that it is as late as 1965 that the leaders of the Conservative Party were first elected by all members of the parliamentary party (previous the choice was in the hands of a small group).
In the last 50 years (I stretch it by a few months) - Macmillan (1957); Douglas Home (1963); Callaghan (1976); and Major (1990) became Prime Minister after their predecessor stood down from the Premiership (all our other Prime Ministers were chosen while their party was in opposition and came to power after a General Election).
This time a Prime Minister will be elected by Labour Party members. The timetable so far is
Sunday 13th May - the Labour Party's National Executive Committee will meet to formally agree the timetable for the elections, including the opening and closing date for nominations and supporting nominations, the freeze date for new members to join the party, as well as the dates for the hustings.
Sunday 24th June - the new Leader and Deputy Leader will be announced at a special Leadership Conference
Wednesday 27th June - Tony Blair will meet the Queen to tender his resignation as Prime Minister. She will then invite the new leader of the Labour Party (as it is the party having a majority of seats in the House of Commons) to become her new Prime Minister.
The Labour Party has set up a special website - http://www.labour.org.uk/leadership/home on which more detailed information about the election and the candidates can be found.