Yes, it can - if your tree is healthy, remove the ivy before it gets any bigger - if you don't, it will eventually entirely cover the tree and choke it. There is a theory that ivy only climbs trees which are either dead, dying or diseased, so you may want to check the health of your tree at the same time.

just cut it at the base to start with is easiest .there are a row of trees next to our common land and everyone has ivy on it for about over a mile long.

No, it won't damage the tree. I know that's controversial, but the only damage it can do is act as a sail in winter, and, IF the tree is weak, or unstable, windy weather can catch the ivy 'sail' and cause the tree to fall. Ivy uses the tree for support only. I does not feed off it, root into it, or otherwise cause it harm. Ivy in a hedge can be a different matter, blocking out light to the lower parts of the hedge, and preventing growth low down in the hedge. I'm sorry to disagree with Bamboo, but it won't 'choke' the tree, only cut out light. Certainly, trim the ivy, and keep it from adding weight to the top of the tree, but it's actually a vital late season nectar provider for many insects (probably in flower now), the berries, ripening in spring, are food for many birds, and being evergreen, it's shelter for hibernating insects and roosting birds.
Phil J

I was about to post that there are two schools of thought on ivy in / on trees, and here they are, set out carefully by two experts.

Read them both and make up your own mind Certo. I would say that a small amount on a tree that's not in an exposed position won't do harm, but cut the stem at ground level when it gets thick and you want to get rid of it. Cut a good chunk - at least an inch - out of the ivy's trunk so that it can't join and regrow. I've had it happen.

the trees near me seam fine its walls you need to worry about

Over the last 12 years I have watched several mature silver birch trees over my garden fence get swallowed up by Ivy ( at different rates) until now most of the trees are covered with thick very dark ivy stems and hardly any of the trees has leaves. Very sad to watch.

ow i agree not a pretty site drc but the trees still seam fine . well you know the ones near me i mean . im sure they could overrun an already ill tree and none of the trees is a silver birch actualy . maybe there is something to this .i like ivy i have it at the front of my house but silver birches are best on there own.realy pretty in the winter . personaly id think you would have to be real carefull even if you had to prune one as you could easily ruin the look of one . theres one near me with the top cut of and it looks terrible .

When we used to have a large woodland garden I used to go round cutting through the ivy stems at ground level on the trees that were most covered in the stuff. It would take some months for the ivy to die off and even longer to fall out of the trees so any birds that were nesting in its cover had time to finish. I would cut through the ivy on about a third of the trees in any summer. That meant that there was always some ivy available for the insects that depend on the nectar and pollen and cover for birds, but the trees didn't get TOO infested. A middle way.

sounds about right beattie i just leave mine till its started to hang down and i get loads of birds .

Phil, when I said "choke" the tree, I didn't mean it would literally strangle it, I meant it would prevent the tree from having its full, leafy canopy and restrict its light and air supply - Ivy up an old tree stump is fine, but if you have a lovely tree, why ruin it by letting ivy second it as a pillar to support itself?

depends on the tree i think