Straw hats were commonly worn by all types of women during the late 18th and early 19th centuries, and they appear in many portraits but are rarely mentioned, possibly because they were so common. Very few survive.
‘They frequently wear high-crowned, broad-rimmed hats; these are usually of beaver, and ornamented with fringed bands; but straw hats are prevalent – some of the same form as the beavers, others less steeple-crowned.’
Mr and Mrs Hall, The Book of South Wales, the Wye, and the Coast, (1861), pp. 300-301
There are a number of illustrations which appear to be of hats made in the shape of a Welsh hat, but made of straw or possibly of some other woven material.
‘Welsh Fishwomen, Llangwn, Pembrokeshire 1st May, 1853′ (Print published by Rock and Co)
South Wales and its staple industries. In 1815, straw hat manufacture was a leading industry in Cardigan, Carmarthen, Haverfordwest, Llanelly, Pembroke Tenby and Swansea. Carmarthen stood at the head of the hat making industry, that is the tall hat, the “hat-bob-cam” which ladies of West Wales patronised even more extensively than did their Lords and Masters. Bridgend was the Paisley of South Wales.
South Wales Daily News, 22.12.1927 [It is not known how accurate this report is.]