Initially apply for the passport at the embassy... once you get that.. pls see apply as a normal dependent visa application ..
pls see the link provided by aruni... esply 7.14
SET7.14 What is the position of Children born in the UK on or after 1 January 1989 but who are not British Citizens?
Immigration Rules paragraphs 304 & 305
ECOs will rarely deal with this category.
Before 1 January 1983, every person born in the United Kingdom was automatically British. The British Nationality Act 1981, which came into effect on 1 January 1983, stated that a person born in the United Kingdom after that date would only be a British Citizen if either of the parents was a British Citizen or was settled in the UK.
A child born in the United Kingdom who is not a British Citizen is subject to immigration control. The parents of such a child will normally regularise the child's immigration status, e.g. by applying to the Home Office to have the child given the same leave to remain as themselves. This means that if the child leaves the United Kingdom with its parents, e.g. for a holiday, re-entry will be allowed within the child's existing leave to remain.
However, there will be instances when a child leaves the United Kingdom without leave to remain having been authorised and therefore requires an entry clearance to return. In these circumstances, the ECO should be satisfied that the applicant meets the conditions set out in paragraph 305.