To get a cheap WAP I bought a Linksys E1200 router from eBuyer - £19.95. For some reason it took about two weeks to get here!?
Anyway, I find Linksys stuff generally reliable, if a bit unpredictable in the interface. However you can usually get there in the end. In this case I eventually realised that I had to "save", before a restart… Range is not great, but you can put them anywhere you can run an ethernet cable (which isn't a problem for me). In this case it is a genuine router, so you can have a different subnet on the wireless side. Also has some more sophisticated settings like being able to check access privileges via a server, so essentially you can control access on an individual basis rather than having one password for all users.
There's a slightly cheaper model, the E900 for £15.95 and there are obviously more expensive models too.
Only wireless N on this router. For me this isn't an issue, because I find I cannot get AC (5GHz) over any distance in this flat anyway. May be possible to link a web of these devices to provide continuous/seamless coverage over a wider area, without switching access points - haven't really looked into it.
Minor gripes: status lights are really well hidden (it would be nice to see some kind of activity without having to pick it up, but then it is also quite unobtrusive), no mounting options (there are no screw slots on the back, so you can't hang it on a wall - you'd have to get the velcro out).
