I'm assuming from the OP's location that this is a return home. Given the bags are in LHR (presumably there's nothing to say they weren't loaded, so they're not officially lost) and the OP would get them back if prepared to wait long enough on the same day, this all probably falls under goodwill and I'm not confident the Montreal Protocol applies here.

BA has been known to push back on luggage claims when returning to your home, even when Montreal clearly applies, and I can see - given they would already have incurred costs getting a courier to deliver them - that they might well not automatically pay out on any further expense, particularly if it's for items that they might reasonably expect you to have at home already.

This would certainly be a situation where I'd spend the absolute bare minimum, just in case.

EDIT: I see, happily, the bags arrived while I was tying. OP, at 90 minutes I think that's worth a short complaint note to BA to see how many Avios they might chuck your way.