Ajax error when trying to view relationships

I am running WP 4.6.1 and Civi 4.7.11 but the problem also existed in WP 4.6 with Civi 4.7.10 and also WP 4.6.1 with Civi 4.7.10. I upgraded to 4.7.11 in the hope that it would fix the problem, but it hasn't!

I search and locate a contact, and view the tabs. The count in the Relationships tab is correct (e.g., Relationships 66) but when I click on the relationships tab to view, I get the error message as per the screen shot attached. No relationships are displayed. Smart Groups are also behaving sporadically.

The relationships clearly exist in Civi (I can browse the table, and the count is accurate) but without the ability to view the relationships, this renders Civi virtually inoperable for us - hence the critical priority indication above.

Steps attempted:
1. Reproduction on the demo site - not possible since the versions of WP and Civi don't match my configuration
2. I have looked at http://datatables.net/tn/7 (mentioned in the error message) and followed the instructions there - the error is a 404 on the ajax feed.
3. My symptoms match exactly those in this case: http://civicrm.stackexchange.com/questions/14442/ajax-error-when-viewing-contact-groups/14768#14768 - i.e., the suspect request URL is identical, the request type is html, both are GET requests.
4. I have looked at: https://forum.civicrm.org/index.php?topic=35447.0 and checked that the patches referenced there are in my set-up - they are.
5. Cleared caches in both Civi and the browser (multiple times)
6. Looked at http://civicrm.stackexchange.com/questions/9522/ajax-error-when-trying-to-view-relationships-tab - symptoms are the same, but I have a 404 error (not 403) and I'm not running Modsec, as far as I know.

Happy to assist in any way I can with solving this, but no idea where to look next!
[Added second image 11/09/2016 to show the Ajax string that can't be found.]