The airline has to pay the tax based on which cabin people sit. It is 20 GBP for people seated in the lowest cabin class (usually coach/economy) and 40 GBP for any seated in a higher class of cabin (usually business, first class etc). This tax is not payable if you are only in transit in London, meaning a stay of less than 24 hours.

So in the past, AA had been absorbing this higher tax amount for people upgrading. Now they have decided to have the passenger pay the additional tax instead of AA. Fair enough I think.

As far as I know, London (LHR and LGW) is the only place where the tax varies based on cabin class. This was always an interesting point for Concorde passengers. Since Concorde was a single class aircraft, all passengers only had to pay the 20 GBP amount since the BA Supersonic Class (R) was in fact the lowest cabin class on the aircraft.

To avoid this tax on my last DONE4 trip, I used my Europe segments to spend the weekend in Helsinki rather than London, and just transited London three times with each stay less than 24 hours. I flew JFK-LHR-HEL, then HEL-LHR-FRA, then FRA-LHR-SIN, making maximum use of the LHR T4 arrivals lounge, T1 and T4 F lounges.