NIck: First, welcome to the forum.
Second, the issue of poor finish crops up on a regular basis on the forum, both for turning and milling. The vast majority of finish issues are cleared up by taking care of two factors; material and tooling.
Material first; all steel is not created equal. Some types are easy to machine and some are difficult, and some manufacturers produce poor quality material of any sort. So stage one would be to dump the indeterminate steel and buy a length of steel of a known grade, preferably EN1A, as that should be easy to machine. It will be cheaper to buy a standard length from a commercial supplier, and there's also a good chance you'll get what you paid for.
As for the tooling you don't say what type you are using, HSS, brazed carbide or carbide inserts? There are two rules for cutting tools, irrespective of the type:
1. Don't bother buying cheap cutting tools, they may be cheap but they are poor value
2. See rule 1
Of course even a decent cutting tool needs to be properly ground, at the correct height and running with appropriate speeds and feedrates.
The problem is unlikely to the lathe itself, although going over to check gibs wouldn't do any harm.
Lastly if we knew roughly where you are based there might be some-one local who could assist.
Regards,
Andrew