BS 476: Part 8 was a test standard, not a code of practice or performance standard, so unless you have test certificates for the doorsets you cannot 'prove' that the doorsets would have the relevant performance or not. BS 8214 guides you in designing a door construction that is to be tested, and gives recommendations for the installation and maintenance of such doorsets; it doesn't tell you how to assess whether existing doorsets comply.
Having said all the above, if the doors are solid timber, 44mm thick or more, are unglazed, aren't large, have steel hinges, are single leaf, have less than 3mm gaps across the head and long edges, you might be able to pursuade the FB that they are good enough. English Heritage used to have a publication that gave useful 'best practice' advice, that you might be able to use, and TRADA do "Fire resisting doorsets by upgrading", or you could try getting some supporting technical evidence from those companies that offer products to be used for upgrading - just Google "fire door upgrade".
Even if you replace the doors, don't get too hung up about the frames - if they're fairly decent close-grained timber, are 32mm thick or more and there are no gaps between frame and wall they should be OK. Again - use the TRADA document or the manufacturer's literature to support performance.
It would be a different matter for FD60 doors - no-one has ever been able to convince me that you can upgrade these reliably and if they're protecting high risks then replacement must be a serious consideration.