Cut it down and dig out the roots, or poison the roots you can't get out by drilling into them and applying SBK - and if you use SBK, wear gloves, don't spill it on the soil, and don't replant for 6 months.

We had an old dividing hedge, fairly big it was too....My husband spent quite a few weeks digging it out, can be hard work, but i think its the best solution...:>)

I hope it is your hedge?

I had great success with copper nails in Ivy. Hack it down, drive the nails into the stump & worry about the roots in a couple of months when it's warmer & hopefully they've lost all sign of life.

Good point, Volunteer!