Ok, more info on using SSL without plugin support:
Forcing https
This is a tipical apache configuration, done with mod_rewrite
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteCond %{HTTPS} off
RewriteRule ^ https://%{HTTP_HOST}%{REQUEST_URI} [R=301,L,QSA]
</IfModule>
Fixing mixed contents
You have to change database entry like http://your.site to https://your.site excluding what you find in the guid columns, so a search/replace in the db dump is dangerous (must me done with care).
The wp-cli solution is
wp search-replace 'http://your.site' 'https://your.site' --skip-columns=guid --dry-run
to test things and
wp search-replace 'http://your.site' 'https://your.site' --skip-columns=guid
to do the job.