I can't tell if my co.uk name has transferred to Cloudflare

There is a similar question here…

At the moment the tag hasn’t changed, so check it has actually be set at 123-reg to CLOUDFLARE. When I last did this the tag change showed straight away, but maybe things have changed (as yours is the second today so I’m doubting myself!).

You can create a Nominet account (use the email the domain is registered to) to see what they say the tag is…

That your site is still working probably means the tag hasn’t changed, as 123-reg say they remove the DNS within 48 hours of a tag change.