I would advise against making any rush decision – unless you're in a hurry or see something really good come up locally, watch all used lathes on ebay (check the completed/sold listings too) and homeworkshop.org.uk and on the small ads here for a few weeks before you buy to get an idea of the market first. Also ask around in local engineering circles maybe for retiring and/or sadly deceased engineers… You have a relatively generous budget so there will always be options.
Buying new is appealing as you won't have to worry about possible wear, but that's not as much of an issue as it might appear. And you do tend to get a lot more metal for your money if you go secondhand, especially for a floor standing size lathe – and look for a machine with a lot of 'kit' with it too, so you're not stuck for hard to find (and/or expensive) accessories later. A decent brand secondhand machine is certainly my preference…
If some kind person here could confirm the overall length is under five feet, I would say watch ebay for a Boxford – read up here:
http://www.lathes.co.uk/boxford/index.html
and as you'll see they're plentiful second hand, so parts, accessories and advice are easily available. Ideally you want the AUD for its floor standing (cabinet) mount and the 'A' signifies the screwcutting gearbox which you will definitely appreciate in due course rather than changegears. Though the price is perhaps a tad high (and it's for collection from Somerset, which may or may not be any good depending on where you are) look at e.g.
http://www.ebay.co.uk/itm/271501285021
for an example of the kind of bundle of kit you should be trying to find with whatever lathe you buy. Chucks, faceplate, steadies are the main ones. Ideally a quick change toolpost system with as many holders as possible would be good. But the more bits the better, means you can get started without further expenditure and delay.
If you're electrically minded don't rule out three phase BTW – not a huge expense to power via an inverter and gain variable speed and smoother running. But that can always wait for later.
Also suggest you get a copy of Sparey's 'Amateur's Lathe' – excellent beginners book on lathe work.
If you're not intimidated by a more 'serious' machine you could even consider a Colchester Chipmaster! Should be under five feet long I'm fairly sure:
http://www.lathes.co.uk/chipmaster/
Less demand for this weight of machine so they often go for a song. Transport (and three phase) puts most people off but there are various ways and means to transport/move these larger machines – including hiring an expert, which your budget would likely cover – ask again here if it's an issue.