I know this is not much use to you, but I include anyway, if only to highlight just what a rip off London's airports are.
At Bangkok's new airport, the daily rate for short term parking, with no limit on the number of days, is Stg3.50, which gets you a space within 100m of the terminal. The long term rate is Stg2 per day (with a maximum of Stg8.60 per month), but that is 2km away.
In Singapore, the short term rate is Stg5.35 per day (SDG15).