https://www.gov.uk/government/publicati ... accessible
"This guide is for people who have renounced British citizenship or citizenship of the United Kingdom and Colonies and who now wish to resume citizenship and be registered as British citizens."
"Do you have a right to registration?
You have a right (once only) to be registered as a British citizen if you previously renounced British citizenship in order to keep or acquire another citizenship."
<subject to the other restrictions listed in the document>
You have a separate right (once only) to be registered as a British citizen if you previously renounced citizenship of the United Kingdom and Colonies:
in order to keep or acquire the citizenship of a Commonwealth country, or
because you had reasonable cause to believe that you would be deprived of your citizenship of a Commonwealth country if you did not renounce.
If you renounced citizenship for any other reason, or if you have already renounced and resumed British citizenship (as a right), registration is at the discretion of the Home Secretary. Registration will be granted if they see fit."
"Effect of registration on present citizenship
You do not have to give up your present citizenship or nationality to become a British citizen. But under the nationality laws of some countries, a person automatically loses their existing nationality if they become a citizen of another country. Before you apply for British citizenship you should consider checking what your position would be with the authorities of the country of which you are a citizen."
If you do re-Naturalize, then your Japanese Citizenship will be immediately forfeit.
Article 11 of the Japanese Nationality Law refers:
https://www.moj.go.jp/ENGLISH/information/tnl-01.html
"(Loss of nationality)
Article 11.
1. A Japanese national shall lose Japanese nationality when he or she acquires a foreign nationality by his or her own choice.
2. A Japanese national having a foreign nationality shall lose Japanese nationality if he or she chooses the foreign nationality in accordance with the laws of the foreign country concerned."
This is not the same as being Dual from Birth.