Lost property on a BA plane should eventually make its way to:
https://smartecarte.co.uk/services/lost-property/

It may take a day or two to be logged into the system.

As a BA Gold, smarte carte should waive the fee they charge.

See any of the many lost property threads:
https://www.flyertalk.com/forum/brit...operty-t5.html
https://www.flyertalk.com/forum/brit...ht-lhr-t5.html