As for the http vs. https bit, and depending on your familiarity with Zen Cart and editing code, check your template's common/html_header.php file where it is linking to css and javascript files. They're linking using NONSSL but should be linked using SSL since I'm on the SSL site. It's supposed to link to which ever one you're using; http or https, but it appears only to be linking using non-SSL (http). On a secure site these insecure links don't get trusted by the browser (and hence don't get downloaded - and hence cause grief.).
One workaround depending on your template (I haven't looked at Westminster) is to change the HTTP_SERVER constant in configure.php to be the same as the HTTPS_SERVER constant, so your site only ever uses SSL. This should be the ZC default IMO.
Code:
define('HTTP_SERVER', 'https://www.selfbuildplans.co.uk');
define('HTTPS_SERVER', 'https://www.selfbuildplans.co.uk');
Looking closer at your code now, if files aren't loading because they're not linked to properly (using https) it could cause the jQuery error shown in the browser console.
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