Is there a limit to how long the British Prime Minister may be in office?

A UK Government is elected for a period of five years.
The five years run from the first meeting of Parliament following the general election.
Unlike the U.S., there are no term limits.

The Prime Minister can stay in office as long as he/she
a) wins the election
b) has the backing of his party to remain as leader

No - there is no equivalent of the US two terms of office and you're out. A PM can remain in office provided he can continue to win elections (which must be held at intervals of not more than 5 years and 1 month) and command the confidence of his/her party. Mrs Thatcher was the longest serving 20th century PM with 11 years. She never lost a General Election but resigned before she was removed by her own party.

http://historylists.org/events/10-key-events-that-led-to-margaret-thatchers-resignation.html
http://www.nytimes.com/1990/11/23/world/change-britain-thatcher-says-she-ll-quit-11-1-2-years-prime-minister-ended-party.html?pagewanted=all