All the Hornby Pullman models I have seen, both the older unlit types, and the newer lit versions, have the roof and body moulded as one piece, so a careful repaint is in order. A matt white paint will do the job, either acrylic from a maker like Tamiya (advantage here is that being water based removal of any paint accidently put on the bodysides should be straightforward) or enamel such as from Humbrol (spirit based so will need more care, but does tend to brush on a little more easily).
Personally, if this is a steam worked train (and the Pullmans Hornby make are essentially steam era stock) I would be painting the white roofs mucky grey brown: they did not stay white in service very long!