the only other way is asphalt it or replace the concrete with a working dpm, asphalt is easier and cheaper short term although you can't bond solid wood to it.
you shouldn't nail down any board over 150mm personally i'd say 130mm as they have too much movement and should be bonded direct to subfloor mate also narrow boards under 110mm wide should be bonded too.
any pre 1965 house didn't need a dpm by building regs so chances are very high you don't have one, ANY floorcovering requires you to have a working dpm whether a sheet set under the concrete or asphalt over the surface although asphalt is quite soft and will prevent you fitting tile or wood onto...
any pre 1965 house didn't need a dpm by building regs so chances are very high neither of you have them, slate isn't impervious it's actually one of the most porous tiles you can buy plus the adhesives are all cementuous apart from epoxy's which you don't want to touch. ANY floorcovering...
the minimum expansion gap you should ever leave is 10mm not 6-8mm so a thin pine beading will not be suitable the scotia is the way to go but instead of getting a wood look, go with a white one and overpaint it this will give you the best finish without removing your skirting.
there is a 90% chance of asbestos in a property of that age also I would guess the bitumen was your dpm, there's a good chance if that's failed you will need to dig up your concrete and redo it with a working dpm
one of these
http://www.damp-meter-direct.co.uk/protimeter-mms2.htm#.UQrrIPL3OJU
or one of these
http://www.buybrandtools.com/acatalog/Tramex-CMExpert-Moisture-Humidity-Meter-Kit.html
not cheap but are really required to install flooring of any type.
and for testing air...
for something proper buy a protimeter mms or hygromaster to test air humidity, by the by the boards to be fitted at 200mm wide are too wide for nailing and need bonding direct to the subfloor and any length over 8mtr and width of 7mtr require splitting and allowing a expansion gap.
that's rising damp mate, need to dig up subfloor new concrete base, dpm leave 30 days then screed and surface membrane that should help fix the problem. You could asphalt but it will eventually fail one day and you'll need to do it again although it is the cheaper immediate option. also see if...