This is not a case of an absence of a reference. The reference (the Wikipedia article exists). And the reference (as do other sources) does provide the answer.
While the Wikipedia article doesn't explicitly say anything about his writing Doctor Who episodes, it would be highly surprising if it omitted that fact, since both his writing and his involvement in Doctor Who are central topics of the article. IMDB doesn't mention his writing any episode either, and it's supposed to be complete. So yes, this is a general reference question; IMDB answers it authoritatively, and Wikipedia answers it with a high presumption of correctness. A high presumption of correctness is sufficient to close the question anyway — general references can be wrong now and then, but the question should provide some justification for doubting it.
Steve Cole's own website is yet another confirmation that he did not write any episode. That's yet another confirmation.
The information is far easier to find elsewhere on the Internet than on Stack Exchange. That's the point of the general reference close reason. Yes, this is a general reference question.