Is it possible to search with google.co.uk with https?
As typing "https://www.google.co.uk" just redirects to plain old "http://www.google.co.uk" I'd say you can't at the moment.
If you go to "https://www.google.com" you should notice that it says "beta" on the logo:
Therefore, I wouldn't expect it to be rolled out globally just yet. Once it leaves beta I'd hope that the country specific secure sites would become available.