While I understand check-in times, when you need assistance, you try to get to the airport early as things just take longer. I expected there should be a way to get into a wheelchair before the actual check-in. I tweeted this at BA, and their response was "...We'd expect the airport to still be able to provide this even if the check-in desk hasn't opened"
Anyway just reporting back on the overall experience:
After the initial mishap at Vienna, after check-in, waited five minutes for a pusher to come, and she was excellent. She aggressively manoeuvred her way through the crowds taking us through security and immigration. She didn't ask us whether we had lounge access, but took us straight to the gate. At Vienna, lounges are before security - no big deal since VIE lounge is nothing special and preferred being in place for boarding.
It was a bus gate, and before main boarding started, we were collected and placed into a special "bus" that raised us to the right-hand side door, and we were boarded before the general buses arrived.
Upon arrival at LHR, there wasn't a chair waiting at the cabin door, but halfway down the air bridge. Was pushed to the end of the air bridge where we were put into a buggy and driven along the concourse to the next special assistance gathering point. We had to wait about 15 mins for a chair and pusher to then take us to flight connections where they helped us board the bus, but then the chair was taken away.
At T5, there was another assistance point where they advised we could either wait for a pusher, or we could just take a chair and push ourselves. We took the option to push ourselves, and they told us we could take it all the way to the boarding gate. Upon entry to the BA lounge, they told us that we wouldn't be able to push the chair down the air bridge, but would need someone to do that for us.
However, at the actual boarding gate, the attendant told us we could push it to the aircraft door, but I would have to push the chair back up to the mid point of the air bridge. I was happy to do that.
What was annoying was although they pre-boarded us, and we were standing in the area after the boarding pass scanners, they started boarding everyone at the same time they allowed us to board. I thought SOP was that wheelchairs should be boarded first, and then they allow everyone else to board.
Upon arrival at HK, there was someone waiting at the air bridge who stayed with us all the way to car pickup.