These were worn by women especially when working in the fields in England, Wales and Scotland and probably elsewhere. The sides of the hat protected the face and the flap at the back protected the neck from the sun.
A few survive in museum in Wales and they appear in prints, paintings and photographs, but possibly only from the mid- to late-19th century.
Sun hats in Ceredigion Museum, Aberystwyth
Sun hat in Carmarthen Museum (T.76.3259)
Sun hat in Carmarthen Museum (T.76.3471)
The women on the Isle of Man are said to have worn sun bonnets.
McClintock, H.F., Old Irish and Highland Dress and that of the Isle of Man, (1943), p. 171 (but doesn’t give a source for this information)
1893 West Wales
Description of cottage women
‘On their heads they wear neat sun-bonnets of printed calico under which the old women wear prim caps tied with black or coloured fancy ribbons.’
Marie Trevelyan, (pen name of Emma Mary Thomas), Glimpses of Welsh Life and Character (1893), p. 163. It is quite clear that her descriptions of Welsh costumes were based on T. J. Llewelyn Prichard, Twm Shon Catti (Aberystwyth, 1828), pp. 47-48, but he didn’t mention sun bonnets which may not have been worn at the time he was writing.
John Thomas took photographs of at least two women in sun bonnets, both about 1875 (digital images on digido.org.uk, National Library of Wales )
‘Mrs Abirley Westbury’
For more on sun bonnets see History on your head