This is nonsense, what is a "London" airport? You'd never see a quicker rebranding of airport names if this idea was taken seriously!
In the article, James Gore of Bristol airport is quoted as saying "... The majority of London airports are operating at capacity."
That's "bull" isn't it? In the entire UK only LHR is at capacity all the time and LGW at some peak times.
No, the way forward with APD is either a low flat rate as in Ireland, or better still, scrap it entirely as in Denmark and the Netherlands.