BBc red button has live coverage on 10th October. (How they manage that I'm not sure I thought it was over by then - but thats what the schedule says!)
The Horse Channel (streamed over the internet) has coverage more or less every day I think.
British Eurosport has coverage every evening from the 28th to the 1st
Sky 3 and 4 has some coverage as part of the "FEL Equestrian world" magazine slot.
Shay - Thanks so much! Have now updated the Sky package to include British Eurosport - looking forward to watching Burghley this evening, as we were away when it was on.