In that case should I look for manufacturers names on the pulleys and chisel post to get a clue about replacement parts etc.? Or are there companies which sell parts for a "build-your-own"?

The lathe was kind of free with a 4' X 2' bench which also had a (now repaired) Record No. 52 vice - all for £7.50! so I don't mind spending a bit to get it going.