You are welcome to try my 1and1 (INIOS) .htaccess settings for SSL (I am assuming you have an SSL direct from INIOS).

PART 1

Login to your INIOS account, go to Webspace and locate the .htaccess file:

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With care! open the .htaccess file, add the redirect code (lines 1,2 & 3) and place a #sign in front of the existing code (the # sign in PHP means the code that follows on that line is ignored, but not lost!)

HTML Code:
RewriteEngine On 
RewriteCond %{SERVER_PORT} 80 
RewriteRule ^(.*)$ https://initiostar.co.uk/$1 [R,L]


#<IfModule mod_rewrite.c>
#   RewriteEngine On
#   RewriteBase /
#   RewriteCond %{SERVER_PORT} 80
#	RewriteRule ^(.*)$ https://%{HTTP_HOST}/$1 [R,L]
#   RewriteRule ^index\.php$ - [L]
#   RewriteCond %{REQUEST_FILENAME} !-f
#   RewriteCond %{REQUEST_FILENAME} !-d
#   RewriteRule . /index.php [L]
#</IfModule>

Seems like there's a difference between historicedinburghtours.co.uk and www.historicedinburghtours.co.uk and I have no idea what to do. I think this has been a problem in the past (something to do with redirects?) and it may be an issue now.

PART 1
should fix your problem, but it takes time for Google to catch up; thereafter it does not matter whether you search for www.mydomainname or https://mydomainname. Where you have more than one domain make sure you repeat the process for each.

BUT

It takes time also for CDN to pick up the changes, sometimes hours, sometimes a day or more, but clear your own browser cache too - Ctrl F5

PART 2

If you continue to see a difference between "www" and "https" you should clear the CDN Cache: This is explained here: https://www.bryan-myers.com/articles...eveloper-Mode/

Hopefully, this sets you on the correct path. It works for my main domain https://initiostar.co.uk

Gary