My atom netbook and the office's atom desktop both drive me nuts when I try to use them...sooo clunky. They feel significantly slower than my phone these days (atom's from 2010 and phone's last year's galaxy)...I know they're not directly comparable machines, but I really do use my phone to browse the web at home over the netbook when my other half nicks the main laptop.
You can get mini-itx machines that'll run full-spec core i5 chips these days - though prob not for under £300. If you build it yourself though you can get very close on budget and get a 'real' desktop chip in I think.
Have a google for SFF (small form factor) cases and motherboards. Or you can get 'smaller than desktop' boxes that aren't as tiny but will run fullsize mATX and ATX motherboards.
I'm in the process of building an editing PC in an Coolermaster Elite 361 case, it's not as small as SFF cases but it's narrow enough I can hide it behind the sofa!