Dual/multiple nationality, if obtained automatically at birth, has always been accepted by Denmark.
However, a new Danish law about dual/multiple nationality has come into force on 1st September 2015. This means that Danish nationals will now be able to apply for another nationality/further nationalities without losing their Danish citizenship. Those persons who have already lost their Danish nationality will be able to apply to regain it during a 5-year period from 1st September 2015 to 31st August 2020.
Please see the information about dual/multiple nationality
Your child may also have acquired British nationality at birth British nationality
As a general rule, Danish nationals born abroad will have to apply for retention of Danish nationality before the age of 22 The 22-year rule
Children born to a Danish mother and a foreign father in wedlock between 1st January l961 and 1st January 1979 may apply for naturalisation according to the “Princess Rule” Guidelines for the Princess Rule