I can't believe this. It works now!! I had already written everything up, but now I checked again to describe the problem better and suddenly everything worked.
I had rebooted the computer previously and it didn't do anything. Now it had also been turned off in between my two posts and somehow that seems to have helped. Which kind of reminds me of IT coming round and asking you "Have you tried... " and makes me feel a bit stupid. But the more important thing is, it works!
And thanks for the great modules!
Anyway, for the record here is what I had written before, in case somebody has this problem. As I said, it was also happening in various browsers (Ff, IE and Safari) . Still don't understand it.
'If I take and Image Gallery page as an example:
The first problem is with uploading a cover picture. After I click "attach image", there's immediately a message that the album has been saved, but the image doesn't appear. There is no error message of any sort, the image just isn't there.
I can create albums, that all works fine. When I try to upload pictures, it again looks like it is working, and a record is created in the database. In the row of pictures, default images are shown. (looks like a sheet of paper) So I think everything works except for the actual upload.
I then checked a different website which is with a different hosting company, there was the same problem with a simple image upload field. No error message, just no picture being uploaded. In fact, overlapping "replace" and "delete" buttons are appearing, which doesn't look right. On that website it had always worked, and I can't remember changing anything on it. So I have no idea where this is coming from..'
But yeah, seems to work fine now ;)