Extremely unlikely. Golden Eagles are confined to Scotland, although they are in the process of re-introducing them to Ireland. In fact I'm sure that the only place in England you might see one is at the RSPB reserve in Cumbria. Apart from that, Eagles prefer high mountains and open spaces with few trees.
It WAS probably a Buzzard you saw - they're similar in appearance, and although not as large as the Eagle its still a big bird with a wing span of around 4ft, and yes, they have 'trousers' too