UK is also more correct because it includes Northern Ireland and the other smaller islands (which are not in Great Britain, the main island)
The British Indian Ocean Territory and the British Antarctic Territory are both British Overseas Territories, but unlike the Falklands, Bermuda, etc, do not have their own ISO codes.
So the determination is more complex than that.
Claims of Antarctic territory aren't recognised internationally, so the codes were removed, but it used to have the code BQ.