I was affected by the baggage fiasco recently (waited 2h for bags) and missed the last train from PAD. I asked the customer service help desk and they said a provision was "authororised" by CS that I could claim up to the usual £200 for a hotel (either at LHR or by Paddington). Didn't get anything in writing from them just submitted the online form. Got money back within 1.5 months.

I tried to get a cheap hotel (one on Bath road) etc to be resonable// in case BA ended up not paying, I think if you do that and explain clearly (but consciesely) why you needed the hotel, it should clear fine.