Linkedin you can search using the search functionality it has inside of it. I don't know enough about the way you guys write your addresses to suggest anything else.
It often makes sense to look with only part of your requirements and then review the results for the rest of the requirements. In your case, you might want to search for people with the target titles anywhere in the UK and look at their profiles to verify whether they are close to the target location.
You can search within LinkedIn (take a look at their advanced people search dialog).