"The Mousetrap" by Agatha Christie is the longest running theatre production in the history of the British theatre. When it broke the record, it supplanted the previous title holder, which was - What?

Chu, Chin, Chow, a play by Oscar Asche which opened at His Majesty's theatre on August 31, 1916 and ran for five and a half years.

Only just seen this. Excellent answer!