Just completed a roundtrip CPH-GIG-CPH in CW and had to book mobility assistance due to a knee injury. Prior to the trip I read a few reports about mobility assistance at LHR and reviews were mixed.

Leaving CPH I decided to move around on my crutches due to a relatively short walk. At LHR i was met at the gate by a person from mobility assistance and driven to a mobility assistance center in Terminal A along with an american couple who were complained a lot about their outbound experiences to all the staff and pointing out that they were in First Class and should not have to wait. I waited about 10 minutes and was then driven by wheelchair thru security and to the lounge.

At the lounge the assistance spoke briefly with customer assistance and told me what time I would be picked up again. About an hour before the flight the gate was opened and as it was a short walk, I cancelled mobility assistance and walked using my crutches.
Upon arrival at GIG there was a wheelchair waiting for me at the plane and I was driven thru immigration and helped with my luggage retrieval and then taken thru customs.

So far so good.

Upon departure from GIG I was picked up at checkin by a wheelchair and driven to the lounge. Assistant told me when he would pick me up again. He drove me to the gate and after a short wait I boarded as the first passenger. On arrival in LHR I was driven from the gate to the assistance center in Terminal A and waited for about 15 minutes before being driven to the lounge. Once again it was a nearby gate so I cancelled the assistance and got out my crutches.
At CPH I was met at the gate and driven thru immigration and to luggage pickup.

All in all a very good experience. It is nice to know that you can travel half way around the world despite being physical challenged (even if it is thankfully only temporarily)