Sparrowhawk?

Hi Everyone,

I live in the West Midlands, I was just driving my car along a road in an urban area and a bird of prey swooped down onto a pigeon/dove which was sitting on the pavement. It pinned its prey down so I pulled over to take photos, unfortunately I they are pretty blurry, as I had to be quick while it was struggling with the other bird. The pigeon/dove then managed to get away and the bird of prey flew after it and caught it again mid-air, I was so shocked to have seen it happen, I've never seen anything like this where I live before. Can anyone help please identify which bird of prey it is? ... I was thinking sparrowhawk but I'm not very experienced so not sure... Sorry the pictures aren't very good.

Thanks in advance :)