In reply to Toerag:
fjallraven: looks a dcent shape, but the net is cinched above the brim all the way around so looks a bit daft
craghoppers: looks decent, but can't see where the net is stored (suspect its just under the crown, inwhich case how does it stay off the face) and doesn't include a strap
outdoor research: do another one called a helios with netting. seems to fit most of my criteria, but its £40+