Chris Green pretended :
Should I stay with the white coated hardboard or are there better
(and/or cheaper) alternatives? It needs to be a similar thickness to
the existing 3.2mm hardboard though I guess it could be a bit thicker
without major problems. I want to be able to just put it up ready
finished, I don't want to paint it after installation.

Look up caravan parts suppliers and repairers. You can get thin ply
from them, in plain white, textured or with various coloured patterns.
It rolls up quite tightly, into a 4 foot wide roll without damage so it
is easy to transport - how do I know? I took my car with a large
trailer to collect 3 of 8x4 sheets, only to find it would easily fit
in my car's boot rolled up and tied.