A question, do BA's 777 rated pilots also fly the 787, and if not, what is the reason?
No, apart from some (all?) of the trainers.
The reason generally given by those in the know is that it's down to costs/scheduling of any required differences course and then costs of maintaining recency and scheduling between the two. As a result the company believe that it's financially more efficient to run the fleets separately for the line guys, rather than combine. Once the 787 fleet is up to size it will be a significant fleet in it's own right so I guess the company POV may well be valid.
That said there has beeen a request for some of the 787 pilots with previous 777 time to come back to the 77 this summer due to workload on the fleet...not sure if they got any takers..