google search a local timber merchant or sawmill....i found a price for a 2 x 2 for another project ( i know you dont need that thick ) ....turns out it was a little farm type shop, 8 ft long, was only £1.30 :)
When I did a similar project a few years back I used Treated roof tile batten, its rough sawn, its pressure treated and worked well for framing out. I recovered in white covered hard board. Most of it was put together with one of the "sticks like sh##" type of glues. Depend how much you want to spend, there's lots of specialist stuff out there. Try a builders merchant for the batten.
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