My client has registered with ipage, which is a sister company of fatcow I believe, one of the many 'unlimited' providers which work fine for low traffic sites
I set up another site for them with fatcow a couple of years ago and this has been entirely adequate for their needs.
There is another host I use in the UK, soho-uk.com who allow you to store files above the root directory, still shared hosting, but good suport in my experience, for only slightly more than the others I mentioned.
I will take a look at fasthosts too, thanks for the tip.