Close-boarded roof was pretty common and standard at one point (late C19th to pre-war I think), using feather-edged boards that the tiles hang from, or if slates just nailed on, I guess these could be square-edged but my knowledge runs out there. Would not normally have any felt/underlay.
If your contractor is thrown by a bit of close boarding I would reconsider letting them do anything to the top end of your house... not the most common roofing method but in no way unusual. Clay tiles presumably?
Is this standard construction? The interior 'cladding'(?) seems to be throwing one of the contractors I spoke to.
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