What you are trying to do is often referred as “mapping remote content into the local namespace” and can be achieved by accessing the given (remote or local) content via a reverse proxy.
I you are using Apache (with mod_proxy_html and dependent modules activated) and having access to the virtual host configuration file, you could use the following additional directives (for the page to be accessed by https://mysite.co.uk/news):
RequestHeader unset Accept-Encoding
ProxyHTMLURLMap "/cms/news" "/news" [R]
ProxyPass "/news" "https://mysite.co.uk/cms/news"
ProxyPassReverse "/news" "/cms/news"
This will fetch the content accessed by /news from /cms/news and replace existing links in the news page which refers to /cms/news by /news.
This can be extended by more links and other replacements depending on your needs.
Kirby and its panel is still available at https://mysite.co.uk/cms and https://mysite.co.uk/cms/panel resp.