Thanks for the comment RodG, it now seems to be partly working, when I land on the index pages; www.example.co.uk is in English and www.example.co.uk is in German however as soon as I click on a link on the English site it changes to www.example.de and the German language.
When I go to www.example.de it does stay on the German language however, even when I click a link.
It also appears as the css file and image directory are not being read because the sites are displayed without images and css styling.

I suspect at least there is something wrong with the rewrite rule:

RewriteRule ^(.*)$ index.php?language=de [NC,QSA]

Should the "index.php?language=de" be changed to something different?