It would be useful to see a picture of the finish obtained. If the finish is uniform, but poor, then it is likely to be a metal/tooling issue. However, if the finish is inconsistent, like the curates egg, then it is more likely to be the machine. Is the banding circular, or helical like a screw thread? Some time ago I had issues with very faint multi-start sets of helical bands, which was cured by fixing a broken hold down bolt for the top slide.
The most common brass, in rod form, is CZ121, which should turn very well. If your supplier states the grade that is good, if not who knows what you have. Experience has shown that not all metal is the same, even from commercial metal stockists.
The potential tooling issues depend upon the type of tooling. For HSS then the most likely problem is grinding of the tool. Ideally the top of tool for brass is almost flat. A small radius (anything from a few thou to tens of thou) on the nose of the tool can help give a good finish. What feedrate per rev of the spindle are you using? If you are using carbide, or insert, tooling then the most common problem is the purchase of the cheap multi-tool sets. They are often poorly, and incorrectly, ground. What tooling are you using?
It may help if we knew roughly where in the UK, or world, you are based.
Regards,
Andrew