UK born baby's passport application

Hi,

We had baby born in the UK when both the parents were on ILR. Now parents got their naturlisation applicaton successfull. None of us have British passport yet. As I had plan to apply for British passport at same time for all of us.

My questions are

1. I didnt included middle name while registering baby's birth. Now I want to add middle name before applying baby's first British Passport. How can I amend birth certificate to include middle name?


2. We parents havent got British passports yet as we would be getting our Naturalisation Certificate in next couple of days. In this case
a. what documents should I submit with baby's passport application to prove her British nationality?
b. Is it possible to apply baby's and parents passport togather?

I tried calling passport helpline couple of times but havent got concrete ansnwer.

Seniors pls.