From the RHS website re ivy:
When to tolerate ivy
On most trees that are in sound health and are not being grown for their attractive bark, ivy can be allowed to grow on the trunk without concern for the tree's health or vigour
Ivy is not a parasite like mistletoe and does not penetrate a tree's bark or roots; the short, root-like growths which form along climbing stems are for support only. Its own root system below ground supplies it with water and nutrients and is unlikely to be strongly competitive with the trees on which it is growing. It is also found mainly on established or mature trees where, unlike young trees, some competition can be tolerated
Ivy has much wildlife value. As ground cover in woodland, ivy greatly lessens the effect of frost, enabling birds and woodland creatures to forage in leaf litter during bitter spells. Growing on trees, it provides hiding, roosting, hibernating and nesting places for various animals, birds and insects (including butterflies), particularly during the winter months and in areas where there are few other evergreens. The arboreal form is also an invaluable late nectar source for many pollinating insects