Sam Ward kindly emailed to point out that John Clare did, in fact, see kites around Emmonsails Heath, and Helpston.
He adds: "Identifying which bird Clare's referring to isn't always easy, as puddock can mean kite or common buzzard. In his bird list, though, he notes differences between the flight of the buzzard and the kite."
That suggests that he was familiar with both, so the gamekeeper-accelerated decline of both species must have really set in a little after his time. Buzzard, incidentally, is another bird name that was applied across several species, all of them large and with an appetite for carrion, at different times, which is why it's used as a name for vultures in North America.