Dorsey appeared in the TV series The Unloved, but was best known for his television soap opera roles in Number 96 as Reginald "Daddy" McDonald, and The Young Doctors, as Sir Clifford Langley.

During this period, he also played the ongoing role of Captain Roke in the Australian Broadcasting Corporation-Artransa Film science fiction children's series Phoenix Five (1970).

Beginning in January 1974, Dorsey played the regular role in serial Number 96 of the comedy character Reginald P. MacDonald, often referred to by his wife and daughter as "Daddy".

An officious bureaucrat with the local council, buttoned-down Reg lived a regimented life and liked to speak in acronyms as a sort of verbal shorthand.

He then took the regular role of Vic Marshall in Network Ten's daily soap opera Arcade (1980), a notorious critical and popular failure cancelled after being on air only six weeks.