Hello,
Not a space issue or anything like that, just that the conditions of our educational connection mean hosting sites like this is a bit iffy (is it really only for educational purposes? and what happens when I want to run a competition etc.). Much better to use a commercial provider where far fewer limits exist.
If the site is still slow during the day tomorrow (and pipex haven't returned my request) - I'll move the site back to the server at work until I've tested everything on another provider.
What's really frustrating is that at this time of night all is working fine, so it must be other sites on the same server at pipex that are using up all the resources during the day.