You can click on the image to get a better view of the prey items - and you're in for a surprise! Bear in mind that Sutton is on the outskirts of London, so the Avocet, Black-tailed Godwit, Woodcocks and Lapwings are exotic food compared to the Feral Pigeons, Starlings and Ring-necked Parakeets that might be expected. It is likely that the main source of the waders will be Beddington Sewage Farm (some 2 miles away), although Woodcocks are but a very scarce hard weather visitor there - so maybe the falcons head off to the Surrey heaths (roding birds are still a good seven miles away). It also begs the question as to whether the Woodcocks are being picked off at night time. (Peregrines have been known to leave a nest site after dark).
In the photo above there are the remains of a Great Spotted Woodpecker, which may tie in with an observation that Peter Alfrey made a few weeks ago of one being taken by a Peregrine at Beddington. The very same? I wouldn't bet against it.
The images here were taken by Rob Dolton, who, together with Steve Thomas, I thank for providing the information contained in this post.