Hi everyone, thanks for all the responses. This is the OP with an update.

After digging more deeply, I saw that DWFI's comment was correct.
Although I clicked on "premium economy" on my company's booking page (which uses Concur linked to Carlson Wagonlit's booking engine), the BA option is in booking class W, whereas the cheaper AA option is in booking class O (consolidator fares).

When I clicked on "economy" instead, both the BA and AA option showed up at the same lower price, both listed in booking class O.

So there is either a glitch on the system, or the system just doesnt allow the purchase of WT+ on via AA.

Interestingly, going onto AA's website instead of my company's page, the same dates of the flights are showing horrendous fares that land you on a Y seat, and W fares that are only £150 under the price of a J seat. Fascinating.