Correct! That will NOT work because a RewriteRule can only examine the {REQUEST_URI} string, i.e., www.mydomain.co.uk will NOT be seen by the RewriteRule!
If this is in the same PHYSICAL directory, you’ll need to test the {HTTP_HOST}, too!
RewriteEngine on
RewriteCond %{HTTP_HOST} ^(www/.)mydomain\\.co\\.uk [NC]
RewriteRule ^news/news\\.html$ http://news.mydomain.co.uk/ [R=301,L]