I’d of said a Buzzard. With a chance of another raptor in the area causing the disturbance.
If it was a bright day, the additional therms coming off a built up area.
The hunting seems wrong for hawks and harriers, if it was circling high and sounds the wrong habitat for a Goshawk.
Keeping raptors as pets, seem to be the new staffie, these days, so it could be anything if it’s a captive bird, that’s free flying worked well. In fact many falconers are contracted by town councils to deal with pigeons and other birds seen as vermin.
But if you’re sure it’s not a Buzzard, then it’s likely to be a captive.
My knowledge is however limited on the behaviour of UK raptors, so to give a definite answer, shouldn’t be seen as fact.