I'm not sure you would get away with 240 grit and here's why. If you think about the cutting tool, probable a ball mill where the end is rounded, and imagine it cutting tiny furrows in the material, then the amount of stepover you give it will determine how far it moves across to cut the next furrow. So if the furrows are very close together it will take a very long time to cut and at some point there is a trade off between time to cut and desired finish. There's not a great choice of UK made machines, Exel was the one I was going for before deciding to make one.