Since you were born before 1983 the government's citizenship checker is not that useful.
The first question to answer is whether Australia was a British Overseas Territory in 1952 or not. Unfortunately for you it was not anymore, so you are definitely not a British citizen otherwise than by descent.
Now we have to check whether you are a British citizen by descent. For this the next question to answer is whether your father was a British citizen by descent or a British citizen otherwise than by descent. If he was the latter, then you are already a British citizen, as your father could give you his citizenship. See this other answer on how to obtain a British passport if you would require one.
If your father was a British citizen by descent, then he couldn't have given you his citizenship, and unfortunately before 1983 mothers could not pass on their citizenships. The best you can try to do in this case is to register as a British citizen, which you can do if your mother was a British citizen otherwise than by descent, which she probably was, as she was born in Scotland. See this other answer for more details on this route.
Also note that while you might not be a British Citizen, depending on your current citizenship (as you were born in Australia you probably are at least an Australian citizen), you might have right of abode, which means you can live and work in the UK without needing a visa. The main requirements are:
one of your parents was born in the UK and a citizen of the United Kingdom and colonies when you were born or adopted
This is true, both of your parents were British citizens
you were a Commonwealth citizen on 31 December 1982 and
you didn’t stop being a Commonwealth citizen (even temporarily) at any point after 31 December 1982
If you have Australian citizenship from your birth then this also applies to you.
In this case you can apply for a certificate proving that you have the right of abode in the UK, meaning you can enter, live and work without restrictions in the UK.