So I got through just now after a short hold on the phone. They quoted around £820 explaining it included a £325 amendment fee and I said in the nicest way possible I couldn't justify paying £800+ for two nights in a hotel. She then said could I hold so she could have a look if anything could be done about the amendment fee. To my absolute delight and surprise she came back and said her manager had authorised the amendment fee to be completely waived.
For once common sense prevails. It makes perfect sense for BA to waive that charge and make a little bit more commission on the hotel rather than have me just walk away and say I'll stick with what I have.