Bristol also developed an all-metal version of the F.2A, designated the Bristol M.R.1. Two prototypes were built, the first flying on 23 October, 1917, but the M.R.1 never entered mass production.
On the other hand, the Bristol Burney was named after Charles Burney, one of the Bristol 'family' of designers.
Sadly I cannot find an image of this machine to check. It must be as rare as chickens teeth.