Adam, some thoughts for you to ponder.
You can make small things on a big lathe but you can't make big things on a small lathe.
You will need to spend at least as much as you pay for a lathe for all the tools and add-ons that you will need to make it work. eg, chucks, collets, centres, tools, milling attachments, ball turning tool, micrometers, digital calipers, taps and die sets, reamers, centre drills ad infinitum.
In addition to the lathes already mentioned have a look at the American Taig (known as a Peatol in uk). If you find a little used one with all the add-ons you may get one for around £300. It's possible to make any of the Stuart marine steam engines (with a fair amount of ingenuity) with one of these. Quite portable, takes up little room. The only problem with it is that it is imperial not metric but using a digital calliper/micrometer with an imperial/metric change over button gets around this.
Jerry. You