You need to ensure that the HTTP version of the site's URLs are no longer reachable, Ruth. That means adding a 301-redirect to force all URLs to their HTTPS versions. This is the most likely cause of your issue
To test, simply go to a page URL in the browser address bar and remove the s from the HTTPS and hit enter. Watch what happens. If the address bar shows the automatic change back to the HTTPS version of the URL, you're good. If it doesn't, you'll need to add the redirect.
You should also ensure that all the internal links within the site have been rewritten to use the HTTPS version of the URLs - like menus, sidebars, widgets, and in-content links to other pages.
Hope that helps?
Paul