I've seen a couple of Sparrowhawks in my garden and the thing I noticed most was the bright yellow eye. however, I understand that in older birds the eye can be more orange in colour. If the one you saw had a pigeon then it was probably a female because the male is smaller and will normally only tackle songbirds. The Sparrowhawks I saw had both taken blackbirds. They find a suitable place (which can be on the ground) and literally rip the feathers from their prey before eating it... it's not a pretty sight. I've also noticed that they are quite happy to sit in one spot for some time, which is great if you have some binoculars at hand. Interesting that the one you saw was being mobbed because when I've seen them, everything else was hiding!