I believe this is not the first or only such ban for a helicopter operator. Another helicopter operator (that I know but do not work for) had a flight booked from Luton, after picking up pax from a fixed wing. The fixed wing was late arriving at Luton, so surprise surprise the helicopter was late arriving at Heathrow. The company was banned from LHR for 6 months! No amount of explanation made any difference.
Incidentally, this was not a runway "slot" but a SVFR daytime arrival onto the heli aiming point. [I suspect that the flight greenarrow mentions was similar.] I am not quite sure about the exact number or frequency, but certainly I believe BAA have a severe limit on the number of SVFR helicopter movements at LHR.
I think we are barely tolerated really.