United Kingdom - Passport & Nationality - British Citizenship (Adoption in the UK)
If a child was adopted in the UK after 01/01/1983 and a parent was a British Citizen at the time of the adoption, then that child is a British Citizen. It is a further requirement that the person must have been under the age of 18 at the time of the adoption, though there are some exceptions.
For as long as an adopted child is still a minor (under the age of 18), then this adopted child could be registered as a British citizen if one of the adoptive parents is a British citizen. It is a complex application, and is granted by discretion.
If a parent of one of the adoptive parents was born in the UK, the adopted child could still qualify for the UK Ancestry if they are a) 17 or over and b) hold a Commonwealth passport.