From what I've seen on other domain registrars, many link to nominet.co.uk as an official guide to .co.uk domain names SO I assume they are officially tied into it and if so it makes perfect sense how they had your details.
I would go back to your registrar and check their fine print and such when on such purchase pages (emulate purchasing another .co.uk domain just don't complete the purchase and I'm sure something a popup or info box will be present mentioning nominet somewhere along the way).
https://support.godaddy.com/help/art...te=uk#registry
https://help.fasthosts.co.uk/app/ans...d-restrictions
http://www.nominet.org.uk/uk-domain-...ain-name/rules
On both GoDaddy's page and Fasthosts page they both mention and link to nominet for certain things, for example on Godaddy's page click on
https://support.godaddy.com/help/art...ite=uk#privacy and it specifically mentions it.
So I'm going with YES you need to complete your account and setup on nominet website as it seems pretty official when all other domain registrars and telling you that certain things must be done via nominet

.