Hi Clairwyn - there's no 'appeal' process but if you believe that the home rights notice was entered in error or incorrectly please lodge an
AP1 for alteration of the register with appropriate evidence.
Please send your completed application form to:
HM Land Registry address for applications.
Please see Practice Guide 20: applications under the Family Law Act 1996.
And do seek legal advice as to what rights you both have under the legislation itself