I've seen sparrowhawks take the odd blue tit in my garden, they seem to hang around in the area for a while and then move on to pastures new.
I must addmit it does look pretty horific to watch but there again thats nature, all birds need to eat to survive, but then I thought, I've taken on the responserbility to feed wild birds and attracted predetors into the area too.
What I decided to do was make less easy pickings for birds of prey by placing the bird table in a less exposed place and planted some evergreens near-by, holly is ideal and gives the wee birds much more of a sporting chance and some cover to hide under while they're awaiting their turn at the feeders. All the Best Tbird+