Odd isn't it. We have virtually no buzzards around us yet see them in great profusion in other areas
My area had virtually no buzzards before 1980, maybe an occasional one along the Ox/Wilts ridgeway, & most of these sightings were to the west (closer to the established Wales/Somerset population) Now we see them all the time. Last spring I watched our local pair + one of lasts years young circling & another pair closing in to join them, lots of swooping & calling eventually coming down to treetop height, a sky full of buzzards & all viewed from my garden. The repopulation spread into the area is all natural after years/decades/centuries of 'control' by the farming/gamekeeping/shooting fraternity; they were (still are) considered as vermin, the belief that they kill lambs still exists, but no doubt they do take young birds & if you are raising pheasant ready to be exterminated with a 12 bore I don't doubt its a problem.
The classic UK extermination of a bird population was Red Kite; I was involved in the Chilterns reintroduction in 1989/94, they've now spread all over the area & way beyond. They were exterminated because, like buzzards, they "killed" lambs. Truth is they are carrion eaters, the old traditions of outside lambing with birthing smells & the occasional still born was all too much for hungry kites (& buzzards), hence angry but misguided farmers.
Tobyjug; its the same with your magpies, farmers trapped & shot them as vermin because they predated on game bird chicks & it became a tradition for all farmers to kill them. They are now back to a more or less natural population, but they are magpie & nature intended them to take young birds. Its fascinating watching them mapping out the area for songbird nests & waiting for them to hatch before they raid them. We now have smarter songbirds, although my resident blackbirds seem to be not so smart as they have not had any young yet & are now on there 3rd attempt.
My nearby RSPB reserve is Otmoor. Its amazing how nature takes over given the right conditions; it used to be boggy river flood land & RSPB took it over in 1997 & since then have cut out permanent water channels, scrapes & isolated islands for protected nesting. Apart from its intended use of over wintering for waterfowl (like thousands of them) , we see Merlin, Peregrine, Turtle Dove, Marsh Harrier (we have pairing activity this year so fingers crossed) we have nesting Hobby, & boom-boom, (pun intended) nesting Bittern. All these are naturally repopulated new to the area bird species, just provide the right conditions & nature does the rest.