I wanted to bump this thread as I now have a definitive answer from Lyndsay on this issue:
Originally Posted by BA Executive Club
I can confirm that flights either marketed by or operated by BA count towards the 4 BA sectors for an upgrade or renewal of membership tier.
In addition, flights operated by GB Airways also count towards the 4 BA sectors.
In some cases our systems won't action this automatically, and we may have to arrange a manual upgrade/ renewal.
KRgds
Lyndsay