You must register your child’s birth according to the regulations in the country where the child was born. They will give you a local birth certificate. This local birth certificate should be accepted in the UK, for example when you apply for a passport or register with a school or doctor. You might need to have it translated and certified (external link) if it is not in English. Once you have registered locally you may also be able to register the birth with the UK authorities. You can only do this if the child was born on or after 1 January 1983. You do not need to register with the UK authorities but it means:
the birth will be recorded with the General Register Offices or at the National Records Office of Scotland
you can order a consular birth registration certificate
You can still apply for a UK passport for your child (external link) even if you do not register the birth in the UK.