Call to non-existent resource slowing page load

1. Do you have any plugins installed? If so deactivate them and see if it helps.
2. Revert to Twenty Twelve theme and see if it helps.
3. Check your content/uploads folder and look for any wrongly placed files.

Thanks for your advice Krishna.

I have been digging a little more, and the breakdown of the call in tools.pingdom.com shows the origins as a WordPress codec file in the root: xmlrpc.php

WordPress lists this file as being enabled as standard since 3.5: With WordPress XML-RPC support, you can post to your WordPress blog using many popular Weblog Clients. The XML-RPC system can be extended by WordPress Plugins to modify its behavior.

I’ve tried to rename the file but the bad request still remains. I will work through your 1-3 advice above, as perhaps a plugin is in conflict with WordPress.

I tried deactivating the plugins and switching theme to Twenty Twelve did not make a difference, though I would not feel to confident about examining the content/uploads folders to see if anything there is incorrectly placed. Also downloaded a plugin to disable XML-RPC, but the bad call is still active, and slowing the site load by 2-3 seconds.

Did you try replacing (after deleting) WordPress excepting wp-content folder?

I will keep your suggestion in mind, but I would prefer to locate the problem if possible. I will keep trying to narrow down the cause.

Many thanks for your advice.

Traced the issue to my custom theme as after I cleared the cache on twenty twelve the issue resolved.

Happy to note that you could solve the problem. ??

Yes, and thanks again for your advice Krishna. Slowly but surely my WordPress diagnostic skills are improving, especially with support from the WordPress community!

Everyone starts like that only. The most important thing is that you keep continuing and exploring new possibilities. And perhaps, you can contribute even to further development. Cheers! ??