I did the same thing many years ago.
I used a solicitor to wrap up the formal deed and deal with Land Registry. My ex didn't use a solicitor, but could have done if she wanted to (but there really is no need if everything is already agreed and amicable).
Process is much the same as a house sale, but much faster as there is only one 'party' involved (ie no buyer/seller to/fro to contend with).