This is an interesting one and will be interesting to see how BA handles this.
I know in normal times if you are in F or GGL on a long haul that gets cancelled and BA put you up overnight they usually organise the Sofitel for you (or they have done in the past). Clearly with complete chaos at the moment they are just telling people to get on with it as they just don't have the staff to sort out mass bookings etc......
I think there is an argument that the Sofitel if you are at T5 is just 100 times more convenient than even the Hilton 5 minutes away at T5. Also add in a couple of taxis to get you to and from the hotel and the price difference suddenly gets less and less (yes I know there is the bus but after hanging around half the day with a ruined part holiday and a family messing around with those buses would just be the icing on the cake......)
Also there is the issue of ones own time and the value that has. When I have had trouble late at night at T5 I would generally go for the Hilton because I have a card with them and if it is not too late I can grab something at Mr Todiwala's in the Hilton which I think is a great place for a curry. However, have also done a couple of early am starts from the Sofitel and rolling out of bed onto a plane at 6am has its plus points too......
Honestly - I really don't think BA will be picking too much of a fight here. Clearly if you book a suite at the Ritz they are not going to cover that but anything reasonable I doubt they will have much beef with. What sort of surprises me more is that with all this irrops there was any space at all at the Sofitel! Usually gets rammed in about 10 minutes when this happens.......

FD.