In the refurbished first class cabins they have empower power plugs you can use. They are the same as those used on UA if anyone has had a chance to try them. They are not standard 110V plugs.
I have my own adapter so I am not sure if BA provides them or not.
Note, not all BA first class seats have these. In my experience it is a safe bet that all planes with 4-class service have the refurbished first class seats with power ports.