Back in the 1970s, British mothers could not automatically pass on their citizenship. It wouldn't have been necessary for your mother to have been registered as a U.K. Citizen in 1973 in order to live in Britain- as a New Zealander with a U.K. born mother she already had Right of Abode- but perhaps a far-sighted move either on her part or that of her parents.
Presumably- all this happened before she became an Australian citizen?
To determine whether she became a British citizen "by descent" or not it's necessary to look at Section 14 of the British Nationality Act 1971 and also Section 2 of the Immigration Act 1971, as in force immediately before 1.1.1983.
http://www.legislation.gov.uk/ukpga/1981/61/contents
http://www.legislation.gov.uk/ukpga/197 ... 077_en.pdf (Immigration Act- as originally enacted).
Her certificate was issued by the Home Office (not a Governor or High Commissioner)- so she should be considered "registered in the United Kingdom" and hence had Right of Abode under section 2(1)(a) of the 1971 Act. As a result, as far as I can see from Section 14 of the 1981 Act, she became a British citizen otherwise than by descent on 1.1.1983. Had it been the other way around, and she'd got U.K. citizenship from a British born father rather than her mother- she'd have acquired her Right of Abode under section 2(1)(b) and that would have made her British by descent.
So apparently she's British otherwise than by descent and if you were born in Australia in 1983 or later that makes you a British citizen by descent. Hopefully you're not an Australian federal MP or Senator.
To evidence your own claim to British citizenship- generally a British passport or Right of Abode stamp in an Australian passport would be required.Has your mother got a current British passport?
Also- take great care not to lose the certificate of citizenship because (apparently) the Home Office don't have records for anything before 30 September 1986.
https://www.gov.uk/get-replacement-citi ... ertificate
The National Archives may have copies but it would be unwise to rely on that since not all records may be available.
Since your mother is NZ born- you're also a New Zealand citizen by descent but need to register your NZ citizenship before you can use it.
http://www.citizenship.govt.nz
This is not intended to be legal or professional advice in any jurisdiction.