A bit drastic, I know, but all I can think of is get out of London! The London Plane (Platanus X hispanica) tree is not particularly common elsewhere in Britain: it's just that they were planted in London in huge numbers in the 18th century and survive all the pollution far better than other species. They are an immense asset to the city and it's unlucky that you are allergic and suffer.
Indeed, I believe it's not know what the life expectancy of a London Plane in London is, seeing as few of the original ones planted back then, have yet died!