Thanks for your help Patrick, but something seems to be amiss.
Ok, I use SFTP and apache.
I have already attempted to right click on directory to set permissions.... this is how I normally do it and have in the past. The problem is, it doesn't stick. It just resets itself back to the 'write' being unchecked.
I'm not sure if this has anything to do with the problem.... but in the forum module, you cannot overwrite an uploaded image, but it appends a number on the end of the file name if there happens to be another of the same name... makes sense as lots of users upload in the forum. But as admin, I want to be able to overwrite the image when I need to.
I believe it is something to do with the module. It is only the folders for the forum module which are located in the assets folder.
I don't know if that sheds any light on the situation or not.