The "pretty good idea" (Ellis' "non-secret encryption") was published about in 1969. Clifford Cocks found a workable algorithm for it — using prime factorization as the trapdoor function — in 1973. No cryptosystem was ever developed around the idea, by Cocks or GCHQ in general; they just sat on it as a classified secret. Then, in 1977, RSA was independently invented and published as both an algorithm and a full cryptosystem.

I would definitely say that Cocks and RSA both independently discovered what we refer to as the RSA algorithm. We should maybe call it the Cocks–RSA algorithm.