Outside of the UK, the nearest population of the wasp is in eastern Europe, in Poland and Estonia.
Eilish Rothney says the nest, which has engulfed her ring binders, is about 1m (3.2ft) tall.
Traps are to be set for Asian hornets after the species was found in Wales earlier this year.
Paul Haggett said it was "soul-destroying" to find all his hives left empty at Handley Farm.
The wasp is a non-native species to the UK and poses a risk to honey bees.
Sandi Toksvig asks the panellists how to keep the insects away.
The UK's second most disliked insect created a buzz this summer.
Alison Riley, 34, says she was left in "absolutely agony" after being stung more than 100 times.
The nest with 10 times more radiation than permitted was found at a facility that once produced parts for US nuclear weapons.
