As long as the mother qualifies for transmitting her nationality, the child should automatically be dual national from birth.

The child gets his or her UK nationality from the father and the US nationality from the mother. If the child is born in the UK, the mother should take the child in to the US Consulate to register the overseas birth - and at the same time apply for the child's US social security number and passport.

For the UK passport, you'd just go through the usual procedures for a child born in the UK.

Just be careful - if you're planning on taking the child back to the US (to show off to the family, for example), the child must have a US passport. Chances are they won't deny the child entry - but they will give you a "stern talking to" and waste lots of your time at the Immigration entry point.
Cheers,
Bev

 

https://travel.state.gov/content/tr...considerations/us-citizenship/Acquisition-US-Citizenship-Child-Born-Abroad.html

 

Thank you - do you know anything about applying for both passports at the same time? Is that fine?

 

https://travel.state.gov/content/travel/en/passports/apply-renew-passport/under-16.html

 

https://travel.state.gov/content/travel/en/international-travel/while-abroad/birth-abroad.html

The two links should answer your questions. US citizens enter and leave the US with their US passports.

 

Thank you, sorry if I'm missing something. I want to take my baby to the US 4 months after birth on a US passport, but assume I will need to enter the UK with its UK passport when we return 3 weeks later. So, I am just wondering if its fine that I can apply for my child's UK and US passports simultaneously.

 

Hiya, thanks so much you've been very helpful.