We recently purchased a home that looks out onto a wood ravine. Previous owner decided to plant ivy in the woods and would blow the fall leaves down the ravine. Ugh! I got all the ivy trimmed off the trees. I would prefer a more natural looking woods, but do not want to harm the trees and natural woods plants growing there. If I let the heavy fall leaves to cover the ivy, will they eventually smother it out?

[For some reason I was not able to comment in the OP's thread.]

IME nothing smothers English ivy to death. Once established, it is also impervious to prolonged drought. If you want to eradicate it without herbicides, pulling/digging it up may be your only option. Leaving as little as a fragment may allow the ivy to start over, so don't be surprised if getting rid of it requires a few years' vigilance. If your emphasis is on wildlife gardening, English ivy contributes little to North American ecosystems. Any native woodlander that could be growing there instead would play a natural role in the flora and fauna community.