British consular birth registration

[Tkydon]

If the parent was born in the UK or Dependent Territories and the child was born in Japan,

If you register the Birth at the British Embassy or Consulate, the Birth Certificate will state:

"4. Claim to Citizenship: Section 2 (1)(a) of the British Nationality Act 1981"

https://www.legislation.gov.uk/ukpga/1981/61

2 Acquisition by descent.

(1)A person born outside the United Kingdom and the qualifying territories after commencement shall be a British citizen if at the time of the birth his father or mother—

(a)is a British citizen otherwise than by descent; or

(b)is a British citizen and is serving outside the United Kingdom and the qualifying territories in service to which this paragraph applies, his or her recruitment for that service having taken place in the United Kingdom or a qualifying territory; or

(c)is a British citizen and is serving outside the United Kingdom and the qualifying territories in service under an EU institution, his or her recruitment for that service having taken place in a country which at the time of the recruitment was a member of the European Union.
....

This Consular Birth Certificate serves as permanent proof of British Citizenship, and never expires, unlike a UK Passport.
However, they won't accept it for a UK Passport application. For that, you will need to provide the Japanese Birth Certificate, and a certified translation.