No, 'No Deal' plans will not apply if we leave as planned
"Come Jan 31, if the UK leaves the EU as planned, Brexit will trigger a statutory instrument that changes some text to create a "UK GDPR". The little kingdom's Data Protection Act 2018 will also get tweaked. You can see the expected changes here. ®"
No, your link is to changes planned for "the event the UK leaves the EU without a deal". Come Jan 31, if the UK leaves the EU as planned, 'no deal' plans will not come into effect. Please keep up.
(Unless, of course you're talking about Ben and Holly when you mention a 'little kingdom'.)