best weed/root killer

Hi all,
My garden runs parallel along an unused railway line and i have tried to cut back various trees and shrubs that have encroached onto my side , there is a few hardy shrubs that keep reappearing each year where i want to set up a rockery.
Basically I am looking for recommendations on root killers that will do the job

The people who owned this house before me, dug a trench between the railway fence and lined it with paving slaps on end, because it was the only way to stop the roots - nothing else seemed to stop them.
As long as there is a live top part on the railway side, the roots will keep growing through under the fence, unless you make a barrier to stop them.
If you can cut the tops you can treat the stumps with SBK mixed with paraffin.