Be aware that if you fly into India on your Indian passport and then attempt to fly out on your British passport, you will have issues with the Indian immigration authorities. You may have to pay for an exit visa in addition to a fine and may miss your flight.
As you have time, I would suggest surrendering your Indian passport (about five working days, if you do it in person at VFS) and then get an X-visa (another three-five working days, at VFS).
Also note, as CR001 has pointed out, that the 90 day grace period starts from the date on your naturalisation certificate, not from that of your passport.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.