(a) a British citizen; or
(b) settled in the United Kingdom.
'Settled" means having unconditional or indefinite leave to remain.
Children born before 1 July 2006
Before 1 July 2006 a child could only obtain British citizenship through his/her father if the father was married to his/her mother at the time of the birth. Otherwise, citizenship could only be acquired through the mother.Children born on or after I July 2006
From 1 July 2006 onwards, a man is treated as a "father" of a child for the purposes of British citizenship if
(a) he is married to the mother at the time of the birth, or
(b) he is treated as the father under section 28 of the Human Fertilisation and Embryology Act 1990 [and certain other legislation], or
(c) he can satisfy certain prescribed requirements as regards proof of paternity - i.e.. he is named as the father on a birth certificate issued within 1 year of the child's birth or he can otherwise satisfy the Home Secretary that he is the father of the child (by means of DNA test results, court orders or other relevant evidences.
Thus, a child of an unmarried British citizen father born in the UK on or after 1 July 2006 will be born British, so long as there is proof of paternity.