When you say cheap, how cheap we talking? If on a budget, I would say you probably want to look at Lenovo or Acer.
I've never owned a Lenovo, but I have had Acer laptops before and thought they were pretty good value.
Doing a quick search can find an Acer Aspire Lite 14 with touchscreen for around £500. I can see larger machines but they then look to jump up in price another £200 or so.