Chris
Check that the carriage actually is riding properly on the bed sheers and not partially on the leadscrew. The one I had was so bad that it had worn away much of the inside of the feed nut! Somewhat extreme but lesser instances of the problem are not unknown. Machine is hardly precision fitted so its quite possible for the hamfisted to re-assemble it with negative clearances in unfortunate places. Spindle and tailstock alignment on mine was poor too.
Mine had one of the headstock bearing caps cracked open and cost me two pints of beer and packet of Players back in 1973 or 4. Complete with a full set of change wheels. Way overpriced for the lathe alone but a small writing case full of bits came with it, some worn out tat, some curiosities (Unique pressed tin dial gauge anyone), some useful and two full boxes of 1/4 x 2 1/2 tool steel one stellite, one a good brand. Figured I got my moneys worth in tool steel alone. The Unique was actually rather good.
Unlike the lathe which, bluntly, was pretty desperate device. Once repaired it was possible do reasonable turning work on not too demanding materials but my god it was hard work. Realistically it was originally made down to too low a price. These days its a curiosity. If you actually want to do some turning work save up for something better.
Clive.