I think the first step is to remove the top laye of concrete and see
what is what underneath.

Yes, and replace with a breathable material (ie lime based). The problem
will be where the floorboards meet the hearth - the wood may absorb moisture
through capilliary action. Could just make sure the edges of the
floorboards are "sealed" with beeswax/turps polish or varnish (depending on
whats on there already). Try asking on the discussion forum at
www.periodproperty.co.uk there are lots of knowledgeable people on there.

Mortgage companies don't seem to understand this though, surveyors go
round with electronic devices that measure the slightest bit of damp
in the walls and the mortgage company throws a wobbler.

Absolutely - ******* !! Mortgage companies and most surveyors have no idea
about period property and are the cause of alot of problems (ie insisting on
dpc etc). There are mortgage companies that specialise in period property
but as far as I know they charge a premium. The survey on my house said
that there is damp everywhere but fortunately the mortage company did not
retain any money they just said to sort it out. This we did by removing
lino from quarry tile on earth floors, removing small patches of cement
based renders/plaster where repairs had been made, removing non breathable
wall coverings etc. One winter, one summer and lots of coal fires later we
have no damp.

Never trust anyone with an electronic damp meter - 9 times out of 10 they
are measuring condensation anyway. The only way to determine if there is
damp in a wall (for example) is to take core samples.