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I have an Indian passport with ILR since 2011.

I was going to go on a month's holiday to India for the whole of the upcoming September along with my parents. But some things came up, and now I need the British passport by the time around December-January, therefore I am trying to apply ASAP.

I will be finishing my Life in the UK test very soon, but I have read somewhere I will have to send my current Indian passports as proof of ID for the citizenship application? I have also heard I might have to send my parent's passports too as proof? And on top of that, when do I officially revoke the Indian passport? After I get citizenship or after I apply for my first British passport?

Thanks

You do realise that there is no guarantee you will have your citizenship approved, ceremony attended and passport in that time.

but I have read somewhere I will have to send my current Indian passports as proof of ID for the citizenship application?

Correct but you don't send the originals. You scan and upload your documents before your ukcvas biometrics appointment.

I have also heard I might have to send my parent's passports too as proof?

Rubbish. Don't believe very thing you hear.

And on top of that, when do I officially revoke the Indian passport? After I get citizenship or after I apply for my first British passport?

Likely once you have passport. You should ask these types of questions in the "Other Countries" sub forum further down the main forum page where Indian passport surrender and OCI question are plenty with answers.