I was caught out by the Qatar differing lounge access criteria but on a QR ticket, not a BA one.
The outbound was booked just before travel and I flew home on a different ticket; the return was much cheaper, three months later, and it completely slipped my mind that it was a "P" class.
BA doesn't offer "business lite" fares on its own metal and isn't set up to do the same on Qatar, so I guess it just works better if all BA flight numbers in business class come with full lounge access.
Of course, two new posts appeared between the one I was responding to and mine, in the time I took to type out my previous post.