Anyone can own a .co.uk domain, there are no restrictions. This also applies to .uk (without the .co).
The Cloudflare offering is probably the cheapest (or is going to be the cheapest) registrar in terms of renewals because their plan is to offer them at cost price. I'd see if they're up an running, they said they were going to in one of their latest blog posts.
Other than that, I can't provide a recommendation cause I don't look for the cheapest prices, sorry about that, someone else probably can though...