I am no expert, but they sound very much like Buzzards. A Sparrowhawk is not a 'large bird'. Also the 'bullseye' description fits a Buzzard. Especially when viewed from beneath and sunlight catching the wings.
I was at Leighton Moss in Lancashire on Monday watching Marsh Harriers. Now THEY are large birds and so lovely to see.
Any sighting of large birds circling in the sky is food for the soul.