I have recently just naturalised as a British citizen, however, it will take 7-10 weeks to get a British passport in which I would have to send my current Australian passport and Citizenship certificate as part of British passport application. Due to my mother's ill health, recent hospitalisation & subsequent health deterioration I have put off applying for a British passport as I would be without my current passport which I need to use in order to go back to Australia and visit my mother. My concern is upon returning to the UK (as I no longer have a BRP card which I used to present along with my Australian passport at Immigration), will they let me back into the UK using my Australian passport and showing them my British citizenship certificate? or will I be considered a tourist on an Australian passport and must leave the country within 6 months when tourist visa expires? Please help as time is of the essence.
Whatever happens at the border, two things are certain:
First, if you enter with your Australian passport, even if you get a stamp granting leave to enter, you do not have to leave within six months, because you are a British citizen. You therefore have right of abode in the UK, and any stamp purporting to place limits on your presence in the UK has no effect. You will not be considered a tourist, as a matter of law, even if the officer somehow thinks that you are a tourist (or any other category of foreigner) and stamps your passport accordingly.
Second, if you have to speak to an immigration officer (which you might not need to if you use the automatic passport gate), the immigration officer has to admit you to the UK if you can show that you are a British citizen. Your citizenship certificate should achieve this.
The specific series of events you will encounter at the border is difficult to predict, but you should have little trouble or delay. If they ask you why you didn't get a British passport, you can explain just as you did in this question.
You should also consider the advice in Traveller's helpful comment: if you are planning to be in Australia for a while, you can apply for a British passport while you are there and use it to return to the UK.