I would try an abrasive polish like autoglym super resin first.
^ AG SRP isn't really abrasive at all, its more of a finishing polish and doesn't really have any cutting properties.
And seriously T Cut is rubbish - a car I did last week had been mullered by a car trying to remove a mark with it and looked like he had used sandpaper on it. There are much better abrasive polishes available that break down and therefore don't leave the paint looking so rough.