"Clamping" used to be the original term (1903 onward) for picketing or tying an aircraft down when not in use - to stop it blowing away.
If the weather was foggy, the aircraft would all be "clamped".
The "harry" is a corruption of "Hoorah" or "hooray" which would precede the "Clampers" because we could all go back to the bar or pub.