I wish I had better news, but the last time we flew longhaul with BA it was a bit of a shambles, tbh.
THere was no way to enter dd1 (then 3) on the system as ASD - she could be disabled or not disabled. SO we opted for disabled, to flag up we might need extra help.
This then meant that she was moved away from our pre-booked seats, to sit on her own, by the computer system, as she was unable to be booked into the seats we had aloocated if she was marked on the system as disabled. They only moved her. to sit in a differnet part of the cabin entirely. on her own. at 3.
I had to call every day to make sure she was still seated with us (staff could override the system when I called, but not put a block on her being moved again).
Security at the airport is what it is. We have a letter form our gp, and take along dd1's statement too, in case we need to talk to someone about needing extra space/time whatever. on the whole we have found security to be ok, but obviously there are queues to contend with.
on the plane, staff were good - helpful and tried to ensure we had as good a flight as possible. it was the lead up that was so stressful. nothing could be done about check in, or any of the details we might have needed - the system seemed to be set up to help with physical disabilities only. maybe it has changed in the 5 years since.
other airlines have not necessarily been much better, btw, but I am better prepared, and dd1 is more used ot flying, and so our trips now are relatively smooth.