I've cut away a lot of the leaves towards the bottom of the tree and can see that they are coming from some tree/vine that is growing up my poplar tree. I want to identify what it is and how best to get rid of it. It is probably around 10ft tall now, so I can't reach the leaves and branches that are higher up. If I cut off the branches (that are wrapped around the poplar trunk) from the bottom, will those at the top die off?
Pretty sure this is good ole English or Common Ivy; Hedera helix. A very mature plant that is showing the 'mature' form of leaf that looks different from the original young leaves. pics of English Ivy
This ivy has become a weed in the plant world. Definitely cut all the stems at the ground that supply the vines on the tree. Let them dry up and then cut as much as you can off the tree. Don't worry about the stems that have become part of the bark. Leave them alone. Poplar is a 'weed' tree as well, grows fast, great wind break. Yours looks ancient for a Poplar. 'Weed' trees are called that because they are tough, grow fast and because of the fast growth are short lived compared to other trees. If this tree comes down could it hit your home? If so, I'd be (sadly) removing this tree professionally...with a tree removal company. If it comes down and all it could damage is the fence, I'd leave it. The ivy will hasten its demise. You could get an arborist to actually look and test this tree to make sure it has some healthy years ahead or if it might come down in the next wind or ice storm.
What do you want to do with your ivy? It is healthy, green and free. Just don't allow it to climb up your trees, shrubs. Not great growing on your fence or home but a little looks quaint. Check out that one house in this link completely, I mean completely covered with ivy with just the windows and doors exposed. Amazing. Massively quaint!
It is Ivy (Edera helix).
I heard two theories about ivy climbing trees (which is normal in my region).
One is to keep it. It doesn't hurt the tree, but it keep a nice environment for birds (you can notice that there is a lot of space for nests (and sheltered). I can confirm that in all seasons, but especially on winter such trees are hot spot for birds.
The second one say that ivy can damage trees (own weight and it give a lot of surface, so wind can break trees easier). In that case, usually the ivy is removed on the first five feet (1.5 meters), and left dry. The trunk of ivy will in any case remain, as the scares on bottom part. To do complete removal, it requires a lot of energy (it is very well attached, so careful if you use a ladder.