You have set yourself a budget, which is good. £800 will buy you a lot of machine. I think the other things to ask yourself are how much space you have to site the machine, does it have to be portable, for instance some people want a machine they can place under the bench when not in use, whichrules out pretty much anything beyond mini/micro size.
Second thing you should decide is the size of work you wish to machine, and the levels of accuracy you require. Paying extra for a super accurate machine is a bit pointless if you only need to work within a few thou tolerance.
The best value machines IMO are the light industrial units e.g. Colchester Bantam, Harrison L series etc. A lot of these come out of schools where they saw little use, and build quality was generally far above hobby level machines- they will last a modeller a lifetime (and beyond). However they're heavy and need a semi permanent place of residence, that puts people off.
Less popular machines like Boxfords are nice too, but again are not that small.
The small Chinese lathes are very good for light work. Perfectly fine for most modellers, and nice and easy to stash away.
Warco, Axminster, Chester and Arc Eurotrade sell these new. Gumtree is quite good for S/H lathes, also model engineering clubs often have members machines for sale.