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A child born outside the UK on or after 1 January 1983 will automatically acquire British citizenship by descent if either parent is a British citizen otherwise than by descent at the time of the birth.

From this reference:

"Dual Nationality (Children)

Children born in the United States to a father (or, if born after 31 December 1982 to either a father or a mother) who is a British citizen by birth, registration, naturalisation or settlement in the United Kingdom are British citizens by descent.

Minors who are United States citizens and possess a second nationality by birth or descent do not, under present legislation, stand to lose citizenship of the United States simply because they possess the second nationality. However, if the person concerned should, after reaching full age exercise certain rights or privileges connected with his second nationality, loss of U.S. citizenship may result.

It is considered advisable for parents not to take any steps which may be regarded under U.S. legislation, to be an act conducive to loss of U.S. citizenship. Therefore, it is recommended that parents of British children born in the United States obtain U.S. passports for their children. This will avoid raising doubts about their status as U.S. citizens, and at the same time, after visits abroad, ensure returnability to the United States. For further information contact the U.S. State Department.

In respect of current United Kingdom law such children cannot lose the status of British citizenship without making a formal declaration of renunciation after reaching the age of eighteen years.

The Home Office announced that, with effect from 5 October 1998, children will be required to hold their own passports. Therefore, from that date children will no longer be included on a family member's British passport. We will include children on passports up until then.

Children already included on a British passport will not be affected until the holder's passport is replaced. "

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