As the one who related the second story of a LHR ban, I can confirm that the "problem" lies with BAA and not ATCOs, as far as I can see. Slots and slot times are fairly obviously a necessary evil at very busy IFR airfields for runways. However, for day SVFR LHR helicopter movements an entirely separate aiming point is used that is well away from the runways. It is hard to see how helicopters using this can cause any problems with the runway operations.
I recently attended a helicopter industry meeting with NATS ATCers about operations in the LHR CTR area. I was really impressed with their cooperative attitude and their attempts to find a solution to problems raised. Bearing in mind that we are a side-issue as far as ATC is concerned at LHR, I believe they help us whenever they can.