What is the length of the British prime minister?

Do you mean his HEIGHT, or how long he can be in office?!

If the former, I've no idea how tall the current Prime Minister David Cameron is, but if you're asking how long they can remain in office, then there's no fixed term. Unlike the US President, there's no limit to the amount of time a British Premier can stay in office- elections have to be held every five years (although they CAN be held after four if the governing Party thinks it's got a good chance of getting re-elected then), but the PM can stay on for as long as their health allows and for as long as they have the support both of their Party and the electorate.