As far as I know, all BA flights except the UK Shuttle sevices use the "Speedbird XXX" callsign format (Includes franchise partners (BA/BAW)) And the BA logo is Speedbird.... from BOAC I believe.
However, given the frequency and similarity of the flight numbers for all the UK Shuttle services (Mainly in the range 42xx to 47xx as I remember) a SHTxy format was introduced to reduce the chance of Pilot/ATC errors.
The x was a number depending on the destination (From the second number of the flight number, so Belfast used to be SHT5y)
The y was the "trip" so second flight of the day from LHR to BFS would have been SHT5C. (a, c, e, g.. from LHR and b, d, f... from BFS)
Any BA pilots like to comment ?
Regards,
Shuttlebus
P.S. I'm sure there was a question on this about 4-6 months ago.