Q: obtaining UK passport for child born in Japan (UK/Japanese parents)

[smalldog]

I would also suggest you register your child for the UK Consular Birth Certificate.

Whilst it cannot be used for a Passport Application, it will serve as life-long proof of your child's British Citizenship.

https://www.gov.uk/register-birth-abroad

I did this for the first child then didn't bother for any of the subsequent ones. It is expensive, and ultimately has been pointless so far - never used it at all for the one child who is registered. Their passports are just as good for showing they are British citizens.... YMMV

If you would like your child to have a middle name in the UK then this is an important step and money well spent, as trying to do it retroactively is MUCH harder.