Not jackdaws, folks: we have Mr and Mrs Jackdaw plundering our lawn (she's slightly lighter), and they're smaller than the inkwell crows; and neither are anything like the picture in the Wikipedia page on jackdaws. One clue: I remember hearing "If there's one rook, it's a crow, but if there's two crows, they're rooks" --- and there's a very noisy rookery (or many crows' nests) atop the copse behind the school.

I'll ask around at church, to see if there's a bony-fido ornothologist in the congregation. I'll report results as and when there's results to report.