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!).
https://cf.sjr.org.uk/tools/check?962e881ddbe442a185982106748f2d12

You can create a Nominet account (use the email the domain is registered to) to see what they say the tag is…
https://secure.nominet.org.uk/auth/login.html

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.