Apologies that I cannot link to the installation in question. That is indeed the extra junk I thought might be causing it, and it is indeed added by Page Builder Sandwich. Have deactivated that for now.
It seems primarily to be in widgets. I am using ‘WordPress HTTPS’ plugin to rewrite internal links to https but this does not seem to be working (where it would normally on other themes/frameworks).
For reference, the theme I am encountering this with is Leviathan: http://www.rockettheme.com/wordpress/themes/leviathan
Thank you very much for your rapid response!