How to kill a buddleia?

It's growing in the 8" gap between the greenhouse and the boundary fence
(sheep netting). It's distorted the greenhouse frame, breaking one of
the panes. I've hacked back the buddleia and replaced the pane.

Knowing that buddleias like a good prune I'm assuming it's likely to
carry on growing and cause more damage, so I'd like to kill it. First
thoughts are chemical, but I don't know what to use and how to apply it.

Ideas?

--
Mike Barnes
Cheshire, England