Here is the email I got from the embassy:
Well noted in regards to your intention to apply for an Indonesian citizenship. Please be informed that at the first stage of your application, we are able to issue you with the letter of no objection stating that we do not have any objections for you to apply for the Indonesian citizenship. You will need to come to us in person to apply for such document by bringing your original British passport and the supporting documents (if any) e.g. letter from Immigration and etc. This letter should be submitted when you make an application for the citizenship.
At the second stage, when you have already obtained the Indonesian citizenship, you will be required to get the letter from us to state that you have cancelled your passport with us and that you will renounce your British citizenship. You will still need to come to us for this document and you will be required to present the original of your passport and the certificate of citizenship from the Ministry of Law and Human Rights. Once you have done all of this, you can make an application to renounce your British citizenship with the Home Office in the UK.
The fee for each letter is £50 by Visa or Master debit/credit card. The payment will be made on your visit.
The above process should not be taken as definite depending on the authorities on your area. Some have come to us only to apply for the second letter when they have been given the citizenship. Therefore, grateful if you could confirm of where you are in the process of applying the Indonesian citizenship. You can check with the authorities first to make sure about the letter before you can come to us.
Please advise should you like to apply for the letter from us.
Best regards,
Consular Section | Foreign, Commonwealth, & Development Office
British Embassy Jakarta | Jl. Patra Kuningan Raya Blok L5-6 | Jakarta | Indonesia | 12950