The message
from Klara contains these words:

If anyone has successfully eradicated an
ailanthus, could you tell us how?

Janet Baraclough writes

Like any other suckering tree. Dismantle it, bit by bit if need be.
Cut off the trunk about 18 " above ground, drill holes in its top
surface, apply a stump killer such as SBK *following the instructions on
the pkt to the letter* , cover with a plastic bag to keep
children/pets/rain off. Now is a better time to do it than winter.

Daughter and partner have now done this - apparently the smell was
unbelievable, they both felt ill all day! It did mean, though, that
although they had liked the tree, they were happy to get rid of it!

--
Klara, Gatwick basin