Thanks for replying Ray.
I can only presume that other people are not having this problem, or that they've managed to solve it without posting a message to the forum.
I have also asked the people supplying my server about how to ensure that any new folders created by PHP code are given the appropriate ownership. I am waiting for them to get back to me. It's not so much to do with the permissions, 777, etc., but more to do with who "owns" the folders and files.
The problem is that I've getting "Warning: mkdir() [function.mkdir]: Permission denied..." and "Warning: imagejpeg() [function.imagejpeg]: Unable to open ..." errors on the live server. It works fine on my localhost.
Through some searching I've found a module called "suPHP" which may help with getting the folder ownership correct, however as there have not been any other mentions of this problem I'm wondering if there is another, simpler, solution.