We have two sites:
Both point to the same IP and files.
Is it better SEO practice to direct the user's from example.co.uk to example.com?
Ideally you need a 301 Permanent redirect from one to the other. If you serve the UK exclusively or almost, then redirect from the .com to the .co.uk because the country extension is favored in local searches. Otherwise, redirect the other way around.
Not redirecting creates a vast body of duplicate content which is frowned upon and even penalized by Google. Now, they do not penalize for every bit of duplication and they may even understand multiple TLDs in the way you have them, but if everything is identical, do not risk it.