After painstakingly working through my plugins one by one I find that the wp-ContactForm plugin breaks the media uploader. When the plugin (latest version) is activated, the media uploader gives me the "Are you sure you want to do that?" "Try again" page. Trying again simply loads the Write page into the box.
Deactivating the plugin fixes the problem instantly.
Posting this to help those who have a similar problem...
It is a nasty break - I do rely on the very useful Contact Form.