Call BA, preferrably with the travel agent on the line at the same time. According to BA, there's an authorisation code that can be entered at some point in place of equivalent fare paid to allow the fare class to be changed. They tried to explain the procedure to me last year, but it was all greek to me.
I made the mistake last year of booking the ticket first (as an e-ticket thru a travel agent). And then I called BA to try to apply the award. It took me 3 or 4 calls to BA before I got an agent who was willing to do the extra work to convert the e-ticket to paper and apply the award. (I started that last call by nicely asking for a supervisor immediately, as I had already called in several times. The agent asked me to try to let her help first, and then really went the extra mile.)
If you can book it directly with BA, I suspect it will be less hassle.
Good luck!