The most successful British two-seater of the war was the Bristol Fighter, when flown like a fighter it was the equal of any single-seater - with the added benefit of a gun to protect the pilot's back.
If the Bristol Fighter was the most succesful two-seater, then its leading exponent would have to be the Canadian Andrew McKeever. Along with his various gunners, McKeever scored 31 victories while flying the F2b, more than any other pilot on either side.
Bristol F2b A7227 Captain Keith Park No.48 Sqn RFC September 1917
Following service at Gallipoli, New Zealander Park joined the RFC. Park was unique in that his entire service in the RFC/RAF was spent with No.48 Sqn. He joined as a lowly Lieutenant and rose to become its commanding officer in April 1918. He also was their top-scoring pilot with 20 victories, two of which were in A7227 during September 1917. In WW2 he was AOC No.11 Group during the Battle of Britain.
Bristol F2b A7194 No.1 Sqn AFC Palestine
Many F2bs made it to Palestine where they served with No.1 Sqn AFC and No.111 Sqn RFC/RAF. Some of these may be seen in the colour photographs taken by Frank Hurley in 1918. A7194 is one of these, albeit in a later form with a white fin and black serial. Many F2bs were painted in white as protection from the desert heat.
SOURCES:
Stewart Taylor Photographs Bristol F2b: King of the Two-Seaters; Bowyer, Chaz Windsock magazine 5/4