Hi Navis:
I am no expert on it but I can give you my experience and opinion.
MY passport expired and I made a new one. To be on the safe side I sent them both passport with certified copies so they can return my passport soon. I am not from India and I think there is a issue of Indian Nationality and British Nationality, which I dont know.
Passportexpiration should not have any impact on your status here because you should have received a letter from home office too. That letter give you the right to abode. Always keep that letter as safe as your passport. If you travel keep that letter, old passport and a new passport. Hopefully, you won't need it once you get British passport.
In any case I suggest leave your option open and get a new passport(Indian) and then apply. You will also need your passport for other reasons other than just travel.
With all new procedure it could even take a year(Hopefully not) and then Home Office can still reject(doubly hopefully not). I will always have more then one option if I need to travel in emergency.
Hope this helps.
Waheed