Kennel cough was what I was afraid of when I knew he wasn't choking on anything. But he was eating his food (just ignoring treats) and otherwise behaving normally.
He didn't have a temperature and the coughing noise was the kind of cough he makes when he vomits. The cough that comes with kennel cough is generally a lot more forceful and sustained according to various things I have read/been told.

Anyway, he seems fine today, I haven't heard any cough at all and he's even had a dried liver jerky chew so I think he is ok.

Thanks for your concern about the diagnosis everyone, I know that vets are not infallible!