start with physical removal then as any new growth appears at ground level use a spray bottle with round-up to finish the job.....

Thanks. I started with physical removal. Round up would not affect the hedge?

As new growth emerges from the ivy, you can use a paint brush to apply the herbicide, or...don a couple of pairs of disposable gloves with a cheap cotten pair on top. Dip the gloves in your herbicide mixture and coat the new ivy leaves with your hands.