Google will index and rank whatever it finds.
The correct approach is to use server-side redirects to make the decision for all users of your website.
Without the constraints of your specific setup (you have not mentioned anything), I will give an example of how to do this with .htaccess
(which may not be suitable for your setup):
Create / edit .htaccess
in your site root and include the following:
NOTE: If you have existing code in your .htacess, add this above where there are already rules with a similar starting prefix.
RewriteEngine On
RewriteBase / #this line is not always necessary depending on the host
RewriteCond %{HTTP_HOST} ^publictalksoftware\.co\.uk [NC]
RewriteRule ^(.*)$ https://www.publictalksoftware.co.uk/$1 [L,R=301]
# You can also force SSL with the following two lines added
RewriteCond %{SERVER_PORT} 80
RewriteRule ^(.*)$ https://www.publictalksoftware.co.uk/$1 [R=301,L]
It seems that it is broadly accepted that Google prefers HTTPS websites, for example.
When testing, you should use [R=302,L]
until you are sure that everything is working correctly and then change it to 301.
You should also configure each page to provide a canonical reference specifying your chosen domain and transport as well as the base URL if the same page is available via more than one URL, this is a handy guide.
rel:
https://www.inmotionhosting.com/support/website/htaccess/force-www-htaccess
https://www.inmotionhosting.com/support/website/ssl/how-to-force-https-using-the-htaccess-file