The Lancaster, Hurricanes, MkII, MkV and MkIX Spitfires should all have RR Merlins, the MkXVI should be a Packard.
The Lancaster I/III during war time was produced with the RR Dash 22, or Packard Dash 28/Dash 224. Canadian built Hurricanes similarly had Packard (Dash 29).
It was said a Lancaster you were flying could have each engine produced by a different manufacturer - RR, Packard, Ford, Continental.
What manufacturer/version the BBMF airframes are actually fitted with would require someone in the know. Restored Spitfires have been fitted with commercial versions of the engine. Interestingly the original Buchon was fitted with a commercial version of the Merlin.