Thomas's Fulham doesn't have its own nursery, I think only the one in Clapham does. But an ex-head of Thomas's set up the Kindergartens, a chain of nurseries feeding into it. I found a good overview listing top feeders here - includes tadpoles, chelsea pre-prep, ringerose, pooh's corner etc http://www.londonpreprep.com/2012/08/nurseries/
Too late for the reply but i guess still might be useful- a) Garden house has it's own nursery, the child has to have an assessment prior to the entry, b) Eaton house the Vale is non- selective, thus doesn't have a "feeding nursery" per se, c) Thomas's has its' own nursery I think- but I might be wrong! d) Knightsbridge school has its' own nursery but only for siblings of those who already study at the school, Hope it helps ;).