can the child be british ?

hi guys,
my friend who has been naturalised recently as a result of a marriage to an eea citizen has a dilemma. he had an affair in 2003 and as a result a child was born but the mother clearly said to him at the time that child was not his and the name of her boyfriend was put on the child birth certificate as the father. the child was born in 2004 in uk. last year out of the blue the lady call my friend to let him know that she has just discover as a result of a dna that her boyfriend is not the father and that she is sure that he is the father.
my friend then contacted a solicitor who advised him to do another ho approved dna. he did that and bingo he was the dad and he contacted the registrar office for a change of the father name which was done in january.
his question is can the child be british or does he have to apply for her bc. the mother is foreign national who has applied for asylum
i hope i have given all the infos

See also query about new born whose parents having ILR.