It is really easy to do this via Nominet's system. It costs £12 to change the owner details on Nominet's records but you can change multiple domains to the same limited company at the same time at no additional cost.
Just login to Nominet using link above. You need to login using the email address in the WHOIS admin of your domains. You will need a password (if you haven't already set one use the forgotten password to reset it).
Bear in mind that as a limited company you cannot hide your address in WHOIS so you may want to add Dynadot Privacy afterwards.
You can 'push' a UK domain to another Dynadot account, but the only way to change the Registrant name is through Nominet online services. I believe there is a fee to join.