I will start by congratulating you on having done some historic research.
To start with, it needs to be understood that there are three different statuses at three different times, not all of which correspond on-to-one with each other.
Before 1948, all people born in any of His Majesty's Dominions (including Canada) were British subjects.
From 1st January 1949, a new status was created, Citizen of the United Kingdom and Colonies (CUKC). Only those British subjects born within the UK and its colonies (i.e. not Dominions) or those whose fathers met that requirements became CUKCs. CUKCs were a sub-set of the wider category of British subjects. So not all British subjects were CUKCs, but all CUKCs were British subjects.
On 1st January 1983, yet another status was created, British citizen. Only those CUKCs who were either born or naturalised or registered in the UK or those whose father or grandfather were so born, naturalised or registered in the UK became British citizens. Again, like the example above, not all CUKCs became British citizens. Those CUKCs who failed to become British citizens became British Overseas Citizens, without the right of abode in the UK.
The intent of each of the successive British Nationality Acts (mainly of 1948 and 1981) and of the intervening (Commonwealth) Immigration Acts was specifically to reduce the number of people who had the automatic right to reside in the UK (which is why Brexit really should not have come as a surprise. Controlling the ability of people to arrive in the UK by right predates Brexit by decades. That saying about those who do not study history are bound to repeat it is true).
So, British subjects retained their status even after 1949 (see
Section 1 of the British Nationality Act 1948). But those British subjects without CUKC status became subject to immigration control.
Now, let's look at your situation. You were born in 1945 in Canada. So you were born a British subject. So Section 17 of the British Nationality Act 1948 would be irrelevant, as all it would do is register you as a British subject, which you already were.
On 1st January 1949, you remained a British subject (and post 1983, are a
Commonwealth citizen in UK law), because you were a Canadian citizen (Sections 1(1) and 1(3) of the BNA 1948). But you were not a CUKC, because neither you nor your father were
born (or naturalised) in the UK or its colonies (Section 12(2) of the BNA 1948). Crucially, even if you substitute your mother in place of your father, she does not meet this requirement either. That is to say, the descent of CUKC status outside the UK and colonies was restricted to
one generation from those born or naturalised in the UK.
So you don't have an argument to stand on, either under Section 17 of the BNA 1948 (not applicable to you, because you can't be registered as a British subject which you already were), or of historic legislative unfairness, because the same result occurs even if you were to attempt to inherit a status through your mother instead of your father.
Now, let's have a look at your father. Your father would have become a CUKC on 1st January 1949, because he would have met the requirements of Section 12(2) of the BNA 1948. He would also have had Right of Abode under
Section 2(1)(b)(i) of the Immigration Act 1971 as enacted, and thus, if alive, would have become a British citizen by descent in 1983.
So you may be able to claim Right of Abode in the UK, as a Commonwealth citizen with Right of Abode in the UK, under
Section 2(1)(d) of the Immigration Act 1971 as enacted.
Apply for a CoE-RoA, with your own, your father's and grandfather's birth certificates, and your parents' and grandparents' marriage certificates.
As a Commonwealth citizen with Right of Abode (RoA), you will have almost all the same rights as a British citizen within the UK, except for a British passport and that you could be deported if you committed a crime.
You may find
a thread I had contributed to in 2017, in particular the additional readings at the bottom, to be of interest.
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.
