Originally Posted by DeltaFlyingProf

There is a way. Go to Finnair armed with your BA record locator and have Finnair send you a receipt.
Then you will get a long detail, but at the bottom you will find the old-fashioned fare break down. Base fare, YQ taxes, M information etc...

Edit:
PS: You say using ticket number. My approach requires the booking to still be active with a record locator, so it may not help you. But it is a reason to always get AY to send me a receipt so I have more information about my ticket's fare construction.