When you access your site over HTTPS, it is still loading the scripts and styles over HTTP, this is what is known as “Mixed Content.” This is why your site “appears” to be broken when accessed over HTTPS. Most major, current browsers, will block mixed content resources from being loaded, as a potential security risk.
With the Chrome or Firefox inspector open, we can even see the errors being spit into the console, warning us about the mixed content being blocked, for example :
Mixed Content: The page at 'https://www.exactclean.co.uk/' was loaded over HTTPS, but requested an insecure stylesheet 'https://exact.exactclean.netdna-cdn.com/wp-content/themes/evolve/style.css?ver=4.3.1'. This request has been blocked; the content must be served over HTTPS.
If you intend to serve your entire site over HTTPS, do some research, and be prepared to carry out some technical tasks. And as always, backup your entire site and database before making changes that could potentially lock you out of your site or bring it down.
Here are a few links to tutorial resources that may potentially be of assistance (please read them thoroughly to see if you are comfortable with proceeding on your own):
After reading those articles, and maybe doing a little additional research of your own, if you decide that it’s too technical for you, consider approaching your webhost to see if they have any experience in this area, or consider hiring a WordPress developer on the jobs.wordpress.net board to assist.