Thanks for you time,
For .com, you can choose one of two transfer methods:-
A) A "push" to a new account at the current Registrar. Not all registrars are set up this way, but many are (e.g. Fabulous, NameCheap, Godaddy). You create an account that you control, give the username (but not the password) to the seller and he/she pushes the domains into your account. At which point you should have 100% control over them
OR
B) A transfer to the registrar of your choice. The seller unlocks the domains and confirms the transfer requests you initiated. A few days later, the domains are sitting in your account at the new registrar.
For .co.uk, you MUST go through Nominet (the central body governing all .co.uk registrations). There is a paper-based process requiring documentation from buyer and seller. This is the only way to get 100% full legally binding control over a .co.uk domain name - don't let anyone fob you off with anything less!
A fee of 30 pounds + 17.5% VAT is payable to Nominet for each domain to transfer ownership records, but if they are all owned by the same person and will be transferred to a single new party then you can get away with a multiple transfer transaction which covers 4+ domains (basically as many as you like, as long as they fit the criteria and are transferred all at once) for 70 pounds + 17.5% VAT.
Does this apply to .me.uk, (and/or) .org.uk domains as well?