There shouldn't be anything stopping you, but it will be interesting to see how that goes. There are well over 100,000 .uk domains registered in June by Fasthosts and Ionos 1&1, without the registrants requesting them to do it. Given that registrants are meant to agree to Nominet's terms and conditions before registration, and Registrars are required to obtain that consent, the whole process is quite unorthodox, though sanctioned and blessed by Nominet "to stop cybersquatting".
If you want to, it would be interesting if you could confirm that the move away from Ionos 1&1 goes through alright.