Steer clear of the machines that resurface discs.

They take a minimum of 0.4mm off each side of the disc and if you look at the Mazda MX5 spec. I cannot find a similar Morgan spec it says something like 20mm original thickness at the front for the ventilated disc a minimum thickness of 18mm but a minimum thickness after resurfacing of 18.4 mm otherwise you are taking the disc down to the thickness it should be replaced at.