A quick google gives the number of breeding pairs of buzzards in UK at 70,000
Buzzards prey on small birds and mammals and carrion, (not solely on pheasant)
The number of breeding females of pheasants (a non-native bird) 2,300,000
with 25,000,000 released into the UK each year, with 50% mortality.
Biggest cause of death appears to be foxes, followed by people (driving) and lastly only approx 1-4% of lost pheasants due to raptors...
I'm not aware of all the facts surrounding the arguments but it seems to me after only 20 mins of research that the proposed cull is a bad idea.
Although it MAY make a difference in this instance because this estate MAY have a real problem with buzzards, it will not be the solution in the majority cases.
Others MAY erroneously use this specific example as justification for their own illegal buzzard culls.
If this DOES work due to the specific situation then others MAY try to use it as justification for their own illegal buzzard culls.
Pheasants may be a valuable resource in the 'countryside' but it seems to me that their value is only in terms of what rich people are willing to spend for the thrill of shooting animals. If pheasants were ONLY shot for food then I imagine some clever sod would have started farming them for food only and not to be shot.
I'm all in favor of hunting for food, but hunting wildlife to 'protect' non-endangered pheasants that are only around to be living targets for stupid rich sadists seems morally wrong.