Using my Indian Passport after getting British Citizenship?

This one's a little complicated:

So I recently got my British citizenship but I am planning on travelling to India soon. But instead of returning to Uk straight away, I want to travel from India to Australia. From there I will be coming back to the UK.

I have seen this thread here:
http://www.immigrationboards.com/other- ... 42501.html

and since I am within the grace period of 3 months, using my Indian passport supposedly should not be a problem.

From what I understand from the above thread, I need to use my Indian Passport when leaving the UK and when landing in India. This won't be a problem as Indian passport = Indian Citizen.

But then if I wish to leave India to get to Australia, how do I do that?

Do I use my British Passport, because there is no visa needed to enter Australia on a British passport, or do I use my Indian passport since otherwise the Indian Authorities may ask about a lack of an Indian visa on my British passport? But then if I use my Indian passport, won't the lack of an Australian visa be problematic?

Thanks for any help.

Yes, you'll face issue leaving india for australia.
Better apply for visa and travel to india or perhaps australisan visa on indian passport.