Bullswood

OP reports that grounds for denial of boarding were that "agent would not accept our letter, saying we needed a second letter which said that my wife was fit to fly specifically for this flight."
If the OP produced the original letter as provided outbound, if the agent's reason for refusal is correctly reported, and unless the agent had reason to believe that the pregnant passenger had required medical care during the trip (which is BA's only caveat), then this seems to be an incorrectly based denial of boarding and should be compensated accordingly. Even then, the letter is a recommendation rather than a requirement, and is arguably irrelevant except to the extent that it acts as proof that the pregnant passenger is within the limit of weeks and does not suggest any medical reason not to travel.

I do however feel that BA's wording on the passenger website is woolly beyond the clear week of pregnancy limits, especially given the increasing trend for company policy to be enforced through third party agents (who may at some stations be checking in a variety of airlines with different procedures). What is the force of a "recommendation"? What constitutes a letter written "as close as possible to the travel date" - as a return is covered, just how long a gap between outbound & return is acceptable ? As mentioned in previous posts, no medical professional would be bound by anything other than his/her observations at the time of examination and a statement of the estimated timescales of the pregnancy.

One assumes that the policy wording and training given to contractors mirrors BA.com, which it obviously should do, but who knows... in any case, that would be an issue between BA and its suppliers and does not detract from the OP's case.