Blog entries containing images (using any external editor) won't publish

As the title says, any blog entry I attempt to publish using an external editor that contains an image just won’t publish.

I have tried a number of editors without success, each one errors out with something similar to:

The post web address for the blog was not found:
https://4x4geocachers.com.au/xmlrpc.php
The remote server returned an error: (404) Not Found.

* The images do get uploaded to /public_html/wp-content/uploads/2015/03/ etc. so at least part of the process is working.
* I’m using WordPress 4.1.1
* The theme is 2015
* All plugins are disabled

Please help to diagnose & fix this issue.