British Citizenship -illegitimate child- Mother Illegal

[Hinamalik]

Hi
I am asking this question on behalf of one of my friend. She is Jamaican came to this country in 1999. At the moment she is illegal i.e no immigration status. She has three children from three different fathers, she never got married to anyone of them. Out of three kids , one of the child who was born in 2005, his father is British Citizen, but as stated above she was never married to the guy.

the question is whether the child born in 2005 from a British father ( mother has no status) is able to obtain British citizenship?

They applied for childs passport but the application was refused in 2009 stating that the child was not born from a legitimate relationship. So can an expert throw some light on this issue, it is quite difficult to obtain advice on British Citizenship issue due to their complicated nature.

[vinny]

Children born before 1 July 2006 whose father is a British citizen but not married to their mother - section 3(1) applications.