this will work just not with the caliper you have becose of the bolt spacing.
New TRP Disc Rotor Adaptor for Rear 160mm Disc Rotor. Fit Disc Rotor Size: Rear 160mm.www.ebay.co.uk
problem is i can not find it for sale cheap in any bike shop in stock and only on ebay at near £30 and is the only way to fix this problem.
cable caliper also seem to be a lot wider than hydraulic ones but again modern ones wont match the bolt spacing on the frame so you will need that frame adaptor one way or another.
or take a Dremel to the caliper you have to make the space and grind it down to fit if you only need a few more mm.