I have always tended to go via
hotels.com/britishairways which then redirects onto an affiliate linked uk.hotels.com/....... url but when you finally select a hotel and go to book it, the box for your BAEC number is there on the form. Not sure why I go this way rather than through shopping.ba.com but it has worked in the past and seems to still be live now. Not sure what the earning rate with or without hotels.com rewards are at the moment compare to the figures quoted by
Joeykins