I have just discovered the following on another page of the Citizens Advice link:
Surname. Since October 1997, a surname for the baby is registered when the birth is being registered. The surname registered must be the surname of the father or mother or both. If you want your child to have a surname other than the surname of the father or mother or both, then an application must be made to the Registrar General or a Superintendent Registrar in writing.
This would seem to indicate that one must simply apply in writing to have the hyphenated name indicated above.
Would that be correct ?