Definitely looks like a nuthatch. We get one on a couple of trees in the garden from time to time. I've never heard it's call, though.
Quite a monotonous 'chirp' most of the time. Then, sometimes, a fast warble of almost the same chirp (if that makes sense). They are frequent sightings around here and in the woods. I think we must also have half the county's Green Woodpecker population - people near us say they never see them but we have them most days









