As far as I know, people have good results with oxygen-peroxide, at least with old white parts.
I once did not succeeded with wc-cleaner, another top secret ingredience in lightning up plastic parts, with extremely bleached iglu and western-bank parts.

(nothing got damaged, but it did not magically turn brandnew...)
But do the new parts bleach? The newest bleached part in my collection is the fishers hut, but I guess this house is likely to be ten years old, also...
Maybe playmobil is advancing in their technology...

best,
socrates