1. If the child is born outside the UK to UK Citizen Parent(s) who were born in the UK, then the child is automatically a UK Citizen by Decent.
However, If the child is born outside the UK to UK Citizen Parent(s) who were themselves a UK Citizen by Decent, then the child is not automatically a UK Citizen by Decent, and it would be necessary to apply for Citizenship, which may affect another citizenship such as Japan, where doing so could result in forfeiture of Japanese Citizenship...
However, If the child is born in the UK to UK Citizen Parent(s) who were themselves a UK Citizen by Decent, then the child is a full UK Citizen.
If born to (a) Japanese Parent(s), and correctly registered in Japan, or if the child is born outside Japan, registered at the Japanese Embassy or Consulate WITHIN 90 DAYS of birth, then the child has dual citizenship by birth.
2. You do not have to register the birth of a UK Citizen Child born overseas at the British Embassy, but doing so will provide a Consular Birth Certificate, which confirms the child's UK Citizenship by Decent under Section 2 (1) (a) of the British Nationality Act of 1981 for future reference, so the child can prove UK citizenship even without a passport. There is no deadline to registration, and once registered, this serves as Proof of British Citizenship for life and never expires, unlike a Passport.
However, if a child is born to (a) Japanese Citizen Parent(s) outside Japan, there is a 90 DAY DEADLINE for registration of the birth at the Japanese Embassy of Consulate, and the child will be registered in the Japanese Parent's Koseki Tohon. If the deadline is missed, and the child also has another nationality by birth, the child's Japanese Citizenship by Birth is revoked under Article 12 of the Japanese Nationality Law.
https://www.moj.go.jp/ENGLISH/information/tnl-01.html
"Article 12.
A Japanese national who was born in a foreign country and has acquired a foreign nationality by birth shall lose Japanese nationality retroactively as from the time of birth, unless the Japanese national <'s Parent> clearly indicates his or her volition to reserve Japanese nationality according to the provisions of the Family Registration Law (Law No.224 of 1947). "
https://www.uk.emb-japan.go.jp/itpr_ja/ ... 00050.html
"届出期限
出生の日を含めて3ヶ月以内に届け出る義務があります。
お子様が出生により外国の国籍も取得している場合は、この届出期限を過ぎますと日本国籍を喪失します。期限後には、当館(又は本籍地役場)へ出生届を届け出ることはできませんので、ご注意下さい。"
"Notification deadline
You are required to submit notification within 3 months including the day of birth.
If your child has also acquired a foreign nationality by birth, they will lose their Japanese nationality after this notification deadline. Please note that you will not be able to submit a birth notification to our office (or the registered office) after the deadline."
3. Therefore, your child is entitled to a British Passport.
A UK Consular Birth Certificate is not acceptable for, and cannot be used for a UK Passport application.
You will need to provide the UK National Parent UK Birth Certificate(s), which includes the details of the UK National Parent's parents, and a copy of the UK National Parent's UK Passport picture page.
If the child's mother is not a British Citizen, and the father is, then you also need to prove that you were married when the child was born...
If the UK National Parent(s) were born before 1-Jan-1983, it is not necessary to provide additional documentation of their parents, the child's UK Citizen grand parents.
If you were married in the UK, you need to provide a copy of your UK Marriage Certificate.
If you were married in Japan, or elsewhere, you need to provide a copy of your Japan (or other) Marriage Certificate and a certified translation if the document is not in English.
https://www.gov.uk/get-a-child-passport
https://www.gov.uk/get-a-child-passport ... d-passport
https://www.gov.uk/types-of-british-nationality
https://www.gov.uk/overseas-passports
If the child was born in the UK you can use the UK Birth Certificate for the Passport Application.
If the child was born in Japan, you cannot use the Consular Birth Certificate (though you still should get one), so you will need to provide a copy of at least one of the Japanese Certificate of Delivery / Birth Notification Document / Certificate of Acceptance of Birth Notification - Shussei Shoumeisho / Shussei Todoke / Shussei Todoke Juri Shoumeisho and certified translations, and a copy of the Family Register - Koseki Tohon - and a certified translation.
(I have sent PM introduction to my Certified Translator friend in the UK. Please check your Private Messages)
The details of Japanese Grand Parents are included in the Koseki Tohon. (I did not have to provide any additional information.)
And you need to provide a copy of ALL pages of the child's other current (Japanese and any other) Passport(s).