Mmmmm, good point about checking against ITA. And no it's not. If I use the BA code it is an extra £300 compared to AA code.
Think I may have figured out a way to do it though. I can get the reduced fare on AA .co.uk by using the outbound as BA code share on AA metal and then I have a domestic leg on the return that will give me the 4th qualifying flight I need.
I think!