So what's the issue here?
Presumably there's plenty of stone to be found under the soil.
Could have another shed with the leftovers.
My shed is a bit drier from doing the same kinda thing.
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I don't know anything whatsoever about building, but seems to me a timber shed in a wet stone shed would rot, and besides who wants a suspended floor compared to concrete or whatever.
Can this building be raised whilst you're at it, getting the floor higher than the ground
That would presumably be easier to put a level floor and membrane in and simplify other stuff like doors ect.
Having had a brief look at building an insulated shed from stone,
it seems this is not a done thing.
I guess you folks in the UK do it though, as you folks have older buildings than we do.
Best info I've came across would be stone cladding,
as I've thought about using stone I have for a wee potting/garden shed.
I was toying with the idea of making a block wall inside,
and stone course on the outside (not cladding/stone on edge)
Sorry if I'm derailing the topic, just figured posting this if it may be a consideration?