Shuttle used to denote the specific 'Super Shuttle' service that was introduced in the seventies. This was the good old days when you just turned up without a reservation and if the plane (usually a Trident) was full they would fire up a back up. They even advertised the fact that you might be the only one on that flight but I bet it never happened...
These flights linked Heathrow with Glasgow, Edinburgh, Belfast and Manchester. (Other domestic flights used the Speedbird callsign) Each route had a specific number which someone sadder than me might correct me but I think it was 2/3 to/from MCR, 4/5 to/from BFS, 6/7 to/from GLA and 8/9 to/from EDI. Hence LHR-GLA might have been Shuttle Six Alpha or SH6A - the Alpha being the first shuttle of the day, the next being Bravo, Charlie and so on. GLA-LHR would have been SH7A. (I think the letters lost their significance at some stage and were allocated on a random basis).
Alas, there wasn't a Shuttle One service. This would have given rise to the possibility of the callsign Shuttle One Tango or SH1T for short. That possibility finally went when the two letter SH prefix became a three letter SHT prefix.
Now, as previously stated, the shuttle callsign is applied to all domestic services (apart from Jersey apparently...).