Thanks for all the info. FWIW, here was the text on the Manage My Booking "At the airport" tab, that got my hopes up about the massage
After check-in
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British Airways Terraces Lounge
Location:After Security, the Lounge Pavilion is located in the International Departures lounge. (Lounge access is subject to capacity restrictions.)
Catch up on work before you travel, enjoy a snack or simply unwind in a relaxing area away from the busy airport environment. Molton Brown Travel Spa offers a selection of complimentary treatments.