I have never quite understood why our cabin crew don't do mixed flying.
The Gatwick-based crew does do MFF (mixed fleet flying). This is possible as BA simplified ops some years ago as part of the strategy introduced by Rod Eddington. So, out went planes such as the 767s, with just the 777s (for the Caribbean, Orlando, Tampa and Bermuda), 737s and A319s (for Europe).
Although CC have the variety of long and short-haul routes and faster promotion compared with LHR crew, their pay is poor by comparison. Last year, new LGW recruits were paid I believe a basic of under £11,000 per annum plus allowances. This is one reason why there is always a queue of people wanting to transfer to LHR.