For anyone interested, I have uploaded some photos of the Pet Cemetery in Hyde Park (adjacent to Kensington Gardens), which is mentioned in THe Little White Bird as the "Dog's Cemetery" , which the narrator (Barrie) avoids because of Porthos, his St Bernard.
You can see some of the graves from Bayswater Road but it's not open to passing public, as it's part of Victoria Lodge. If you want to visit it properly, you have to arrange an appointment with the Park Rangers (who will expect a donation for the tour).