Because of this thread, and for the fun of it, I decided to try again if I was offered different rates with or without my A-club number, for a 3-day stay at the LHR Novotel.

And this time they showed me a "3 nights for 2" offer of about 77GBP/night - but only when booking through A-club.com (logged in). On accorhotels.com (without A-club number) the lowest rate was 105GBP/night for the same dates...

I admit that this is the way it should be... better prices for loyal customers...