Hi Mike,
I think you have got the gist of it.
You don't need to fill in a transfer form at Nominet, unless you are also changing the registrant name. I think you probably meant TAG change though.
http://www.nominet.org.uk/registrant...angeregistrar/
The losing registrar should not charge if Nominet make the TAG change for you, unless you owe them money for renewal fees etc.
For the sake of £15 (plus VAT) I would get Nominet to do it too. Bulk TAG changes usually go through in a couple of days.