Buzzards Becoming A Pain!

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I don't know where they are exactly, but there are two buzzards, or at least it sounds like two, at the bottom of the garden somewhere. I hear them every morning, about twenty minutes before dawn, obviously waiting for the first light to come. They are distinctive by their high-pitched "meow" call, so I know they're buzzards. Last year, I found a dead, baby rabbit in my garden, minus its eyes, and with some mutilation to its rear undercarriage. Around it was a circle of its fur. I couldn't for the life of me think how it got there, but I spoke with my neighbour in the downstairs flat, and he said he heard a kind of screech but didn't think any more of it. Still, I couldn't fathom how it got there. Then the calls started coming before early light, and I began to piece two and two together. Then, about a month ago, I went up the garden to hang my washing, and there was a mass of blackbird or crow feathers, but not a single other bird part... no bones, nothing. Well, there was a new cat in the neighbourhood, who took to creeping around under the hedge at the front of the flat, so I shooed it away, thinking what a horrible beast it was, killing off the garden birds. Then, the following week, dove feathers, in my downstairs neighbour's garden, in the same pattern, but quite close to the building... just feathers, nothing more. This was playing on my mind a bit... so many creatures being pounced upon in the garden. Then, it suddenly dawned on me. Next door has three or four very tall birch trees in his garden, and I wondered if the buzzards were perching there, waiting for an opportunity to swoop on these poor, unsuspecting animals and birds as they fed. I know it's nature, but I wish I could find a way to scare the buzzards off. I was worried on Friday, when I went out, and met a friend coming in the gate. We spotted a baby bluet1t on the path, apparently unable to fly. He was trying to hide in the garden plants, obviously afraid of something, and all I could think of was the buzzards, but she and I both agreed that to pick it up and try to rescue it would probably kill it from fright. So we had to go and leave it hopping around. How can we protect these little creatures from the big, bad buzzards? Does anybody know how to deter them, other than getting my neighbour to cut his trees back drastically?