The village green theory proferred by Jonathan has required a lot of research.
I went down to Mitcham Common and there were indeed many different grass types. They didn't appear to be arranged in any discernible patchwork pattern. There was a lot of dog shit, though; much of it pye-dog, I suspect.
No-one at the local library could give me any help with the history of the place. A rather surly assistant did point out that the site of the disappeared Tudor palace of Nonsuch was quite nearby, and that maybe it was there I should be looking for Elizabeth's turf collection.
I think he was winding me up.