I don’t see why there isn’t a feature that would automatically switch you to the HTTPS protocol or was there? It would be nice to have it. Also, it would be nice to have HTTP disabled during the browsing unless it doesn’t support HTTPS. Something like that would be nice.
You can use HSTS, which is accessible form about:net-internals but the web site also has to support this. Alternatively, use HTTPS Everywhere (link for chrome at the bottom of the page). If you really want to force HTTPS, at the cost of not being able to connect to anything else when it’s not available, use the --force-https command line switch to start the browser.