What is UK Citizenship status of two persons born between 2000 and 2006?

Question

I have two children both born in the UK between 2 October 2000 and 29 April 2006. I, their father, am a British citizen, their mother was a US citizen and we were not married.

Between the birth of the first child and the second, their mother was granted indefinite leave to remain.

According to what I can determine from the UK Government website, this:

1. qualifies the youngest for automatic British citizenship as they were born to a British father and mother with indefinite leave to remain.
2. does not qualify the elder as I was not married to their mother and she didn't receive indefinite leave to remain until after the eldest's birth.

https://www.gov.uk/check-british-citizenship/born-in-the-uk-between-2-october-2000-and-29-april-2006

I believe there should be no problem in applying for British citizenship for the eldest simply by filling out Form T, based on the details of this page. https://www.gov.uk/apply-citizenship-born-uk/uk-until-10

You must not have spent more than 90 days outside the UK in each of the first 10 years of your life.

The child has not left the UK at any point.

Is my understanding of this correct?

//Edit - Since this question has been flagged as a duplicate, I must point out that this question is about UK citizenship, not US citizenship. Since the UK and USA do not share laws on who is and is not a citizen, the answer to that other question is not applicable.

Answer 1

I believe you are correct about the children's British citizenship at birth -- the older one did not automatically get British citizenship at birth, and the younger one did. If you and the older child's mother subsequently married after birth, that would have been considered to have legitimated the child, and so the child would automatically have gotten British citizenship according to former section 47(1) of the British Nationality Act of 1981.

If the older child did not get citizenship via legitimation after birth, then you can register the child as a British citizen now using Form UKF, regardless of whether the child lives in the UK or their age.