Unlikely.
The
British Nationality (Cyprus) Order 1960, made under the
Cyprus Act 1960, which gave Cyprus independence from the UK, specified who retained Citizenship of the UK and Colonies (CUKC) and who lost it automatically when Cyprus became independent.
If a person met any of the conditions of Paragraph 2, Section 2 of the Order, they would automatically lose CUKC status and become a Cypriot citizen.
(a)a person who became a British subject under the provisions of the Cyprus (Annexation) Orders in Council, 1914 to 1943; or
(b)a person who was born in the Island of Cyprus on or after the 5th of November, 1914; or
(c)a person descended in the male line from such a person as is referred to in sub-paragraph (a) or (b) of this paragraph.
The certificate shows that your grandfather met the first criteria and so likely lost CUKC status automatically in 1960.
Some people were exempt from this automatic loss of CUKC status, but that was mainly if they, their father or father's father were born outside Cyprus, in the UK or a British colony or protectorate other than Cyprus.
So, where was your grandfather, his father and father's father born?
In any case, even assuming that your grandfather held CUKC status, if he did not hold Right of Abode in the UK in 1983, he would have become a British Overseas Citizen (BOC) without the right to live in the UK. And that status (BOC) is not inheritable. So your father and you would not be able to benefit from it.
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.