No, I think they are all different companies. The ones in T5 now are an improvement on the company we use to have but as you say not satisfactory.
In the USA there is a lot of legislation with regard to the handling of passengers with disabilities and I think this is why the service is better.
Maybe you need to lobby your MP to get it to be the same, here in the UK.
I think it is a low paid job with little job satisfaction and maybe this is why the service is not good. We despair as crew daily with the service we see but it is just one company that gets awarded the contract by the airport authority and there is no way for an airline to use any other provider.
If there was a way of choosing another company and therefore a form of competition, maybe the service would improve.
All I can tell you Notlangley, is that as a crew member I see this on a daily basis. It is soul destroying to care for people for a long time on a flight and then witness them being miss-handled by the wheelchair company! I often see passengers being asked to walk up the jetty because the wheelchair operator finds it too hard to push up the slope!!
At LHR you need to write to the BAA because they are the company that gives out the wheelchair contract and is responsible. Also drop a line to BA customer relations because the staff that deal with these things at BA would be interested to hear your experience as it helps them to push for change. It is only when passengers write in and complain that anything will get done about this.