Hi Andy,
I live in a flat so I've some experience of this. Fortunately, my landlord's not unduly intrusive but your situation seems a bit more constrained. I think the key issues in this situation are:
1. Size of machinery (as David says)
2. Noise — obviously, you don't want to bring the landlord down on you via neighbour complaints.
3. Disguise — can you camouflage your kit if the landlord wants to inspect the flat?
As regards size of machinery, there are lots of small lathes, new and secondhand, you could consider. Have a look at the Lathes UK site here:
Lathes UK
Machines worth looking at are:
Emco Unimat
Hobbymat/Prazzi*
Cowells/Perris*
Peatol/Taig*
Sherline
Proxxon
On the noise front those machines I've asterisked have induction motors which means they are quiet as compared to machines with series-wound motors and DC types. You could also look at the Chinese machines e.g. the Sieg C3 — modest cost + fairly big work envelope for their size but mug up about them before committing. But I don't know how quiet they are — maybe others can comment. As a general principle favour belt driven rather than geared-head machines. Sadly, no boilermaking for you — maybe you can buy one for testing.
As regards disguise, I'm assuming that you have, say, a spare bedroom you can use. Maybe you can disguise this as a 'study' with, apart from bookshelves and stuff, a couple of stout cabinets (e.g. recycled kitchen units) forming a base for your machines and a place to hide them!
Finally, in this situation cleanliness is important, not only as part of disguise but for domestic harmony. Swarf trailed into bed is a definite passion killer!

Joe
Edited By joegib on 14/11/2012 15:58:40