A friend of mine disturbed a bird of prey (I think it was a kestrel or sparrow hawk) that had just killed a pigeon in her back garden. The pigeon was still alive when she found it but died soon after.
If she leaves the pigeon out will the bird of prey return or is it too late now?
The best thing to do would have been not disturb them in the first place, but I do understand the need of this question. So I wouldn't add any advice like "Do not disturb them in the first place".
From what I have seen, Buzzards and other raptors (not specifically the ones you mentioned) would return to kill if left alone. But, provided that it is done quite early before they choose to go away. Many other domesticated birds would join in too, mainly ravens and crows. Raptors usually take care of the uninvited ones.
In my city, Raptors have a typical hunting region where ravens won't happily go to the party.
If its already too late, the poor fellow is anyway going to die in most of the cases. If it is so, You shouldn't:
Edit: I don't know if you should kill it to relieve it off it's pain. There are too many points to consider, example being, is it a rare bird and hence a punishable crime to kill it. I am not really good at things like killing an animal or a bird, I personally would never be able to something like that.
