Oh, uk.co definitely existed for companies. The other 2nd-level domain (besides the academic uk.ac and uk.co) was uk.mod (Ministry of Defence), equivalent to the US .mil. And then, because life is never this simple, things appeared that were neither universities nor companies nor military, so uk.bl was given to the British Library. There might have been others as well, I don't remember.

Back then the code in various pieces of software had hand-written exceptions for domain processing. The joke was that all Computer Science departments in the UK (uk.ac.university-name.cs) ended up in Czechoslovakia.