I don't know what you are talking about as an "open and shut" case. This has to do with the citizenship laws of Hungary, not the UK. Being an EU Citizen is a natural consequence of being the citizen of a Member State of the EU, it is not a matter of qualifying, you either are or you are not.
I attach more info on Hungarian citizenship (this was from 2005 and I don't know if it has changed).
HUNGARY
CITIZENSHIP: Citizenship laws are based upon Law #55 dated June 1, 1993.
BY BIRTH: Birth within the territory of Hungary does not automatically confer citizenship. The
exception is a child born to unknown or stateless parents.
BY DESCENT: Child, at least one of whose parents is a citizen of Hungary, regardless of the
child’s country of birth.
BY NATURALIZATION: Hungarian citizenship may be acquired upon fulfillment of the
following conditions:
Persons with no ethnic ties to Hungary must reside in the country for eight years.
Foreigners who marry Hungarian nationals, or who are parents of Hungarian citizen
minors, or who have been adopted by Hungarian nationals, or who have been recognized
as refugees by Hungarian authorities, need only reside in the country for three years.
Members of an ethnic Hungarian minority of another country need only reside in the
country for one year.
DUAL CITIZENSHIP: RECOGNIZED.
LOSS OF CITIZENSHIP:
VOLUNTARY: Voluntary renunciation of Hungarian citizenship is permitted. Persons seeking
to renounce citizenship must address a written statement to the President of the Republic. The
Embassy can provide information and assistance, but is not able to act for the person.
INVOLUNTARY: The following is grounds for involuntary loss of Hungarian citizenship:
Naturalized citizenship was gained by false statements.