F3G - Your point regarding being "left on your own" by BA, which you later clarified to mean they did not offer you hotel accom in London when they canx the flight, can I ask if you were on a "through ticket" via LHR, or were you just a LHR departure on your return to Paris (I think you said you live in Paris, so were presumably here in the UK on some kind of visit).
If they did - then you have a very strong case against BA providing costs for your enforced overnight stay. The fact that BA cancelled the flight (presumably for reason within their control as it was 4 hours in advance) and could/did not put you onto an alternative flight, either with themselves or others the same day makes them liable.
BA contracted to get you from point A to point B on a set date - they have to do this via whatever reasonable means, or provide you with accomodation and or meal vouchers depending on the length of the delay.