Under current law,  a child born in the UK after 1 January 1983 will only acquire British nationality if either his/her mother or father is:
It used to be the case that only legitimate children could derive nationality from their (British) father, i.e. the father had to be married to mother in order to pass his nationality to the child. This is no longer the case following an amendment to the law which came into force on the 1st of July 2006 . For more information see Question 10 ‘Does the child of an asylum seeker who has a British parent automatically acquire British citizenship?’
What does ‘settled in the UK’ mean?
'Settled' means ordinarily resident in the United Kingdom without being limited under the immigration laws as to how long the person can stay here.
Whether a person is ordinarily resident or not depends on the facts of the case. A person who is not restricted under the immigration laws as to the period for which s/he may remain is probably ordinarily resident if s/he:
Long periods of absence from the United Kingdom (for more than a year, for example) may mean that a person is not ordinarily resident. Shorter periods of absence may also, in some circumstances, mean that a person is no longer ordinarily resident (for example, if he or she left the United Kingdom intending to live abroad permanently).
When a child is not a British citizen at birth
If neither parent is a British citizen or legally settled here, the child will not be a British citizen at birth. A child will not be a British citizen if they have entered the country illegally (for example, without being examined by an Immigration Officer or otherwise in breach of the immigration laws).
If a child does not become a British citizen at birth, he or she may be entitled to registration as a British citizen later.
The child can be registered as a British citizen if, while s/he is a minor (i.e. under 18)--
OR, an application for his registration as a British citizen can be made at any time after s/he has attained the age of ten years, providing that for each of the first ten years of her/his life, the number of days on which s/he was absent from the United Kingdom in that year does not exceed 90.  This may be important to note with regards traveling.
 British Nationality Act 1981, s. 1
 For the purposes of the 1981 Act, in relation to a child born on or after 1 July 2006 (see Nationality Immigration and Asylum Act 2002, s 9 (1) and s 162(5)) a child’s mother is the woman who gives birth to the child, and a child’s father is:
For children born before 1 July 2006, the relationship of father and child is taken to exist only between a man and any legitimate child born to him (a person is deemed legitimated by the marriage of her/his parents)
 British Nationality Act 1981, section 1(4)