How do I get rid of English ivy?

This ivy problem encompasses dozen of square mile in the south Seattle/county area and has been ignored for decades. Our marine climate is ideal for the spread of this noxious stuff. You can't chop a hillside tree down in our town w/o a permit but this stuff causes trees to die all around us here as it grows up the tree and virtually chokes the life out if it in less than a dozen years. It even grew up a utility pole and furled out in the shape of an evergreen tree and had different looking leaves and had dark colored berries. I have dug up rhizomes more than an inch and a quarter in diameter. It travels underground under streets, driveways, and lawns. If left unchecked it will grow into attics, sheds and virtually anything in its way. It can co-exist with other predatory plants like wild blackberry, morning glory, thistle or other vines, and still prosper. I honestly thought of a flame thrower remedy, but the authorities here would lock me up. I even planted a variegated prettier ivy in our front yard but it cannot compete with this stuff. Because it is a very effective ground cover on hillsides that prevents slides and land creep, it gets a pass form most people who live by it but don't have to contend with it on virtually a daily basis. Its the Hydra of plants. You can cut a four inch piece, put in a pot with soil in it and it will root in 2-3 weeks. I cannot express how thoroughly I loathe this plant.