Cashback website Quidco has substantially improved its BA offering. It now pays cashback on almost all BA flights booked via its link, at 1.5% for short-haul and 2% for long-haul. All travel classes qualify, and it does not impact your ability to earn Avios or On Business points from the flight. Only UK domestic flights are excluded. It is not clear if the cashback is based on the base fare or the entire fare including taxes.
A flight and hotel package pays 3%, which means it is worth pricing up the addition of a throw-away hotel for one night to an expensive booking as the extra cashback may offset the hotel cost. Again, it is not clear if the cashback on a package is driven by the base fare for the flight plus the hotel cost, or the value of the entire sale.
Plenty of other airlines are also on Quidco including Flybe and Lufthansa, so it is always worth checking before making a booking. There is a £5 annual membership fee, but this is taken from your earnings and not paid in advance. This is generally a small sum compared to the cashback you can earn, and it pays for decent customer service should you have trouble getting a merchant to pay up.