I have had this issue several times. Once they somehow (we’ll I HUCA’ed several times because I didn’t believe them even though it was a BT ticket and I didn’t know it!) managed to calculate the taxes and UuA.

Since then I have had to call the company TA and book the published fare. Turns out for a semi-flex or fully-flex WTP fare the difference in price between the BT fare and the published BA.com fare was £50. I didn’t have to justify it, they just booked it. It has never been a problem but the TA doesn’t make as much money.