Ed: We recently published an article by Debra Holland about how to treat Ivy on trees. Geraldine Leighton and Andy Davidson point to advice available from the RHS and Woodland Trust on this subject
Debra's article, whilst containing some good information, does not take into account many beneficial aspects of ivy for wildlife and cutting ivy at this time of year when birds are nesting is particularly detrimental.
Also, the flowers which are produced in late summer / early autumn are especially important to bees and other insects as a late source of food before winter.
So, before embarking on the destruction of ivy in your gardens or elsewhere, please read the explanation and balanced advice from the Royal Horticultural Society (rhs) website here with regards to ivy on trees. Also from the Woodland trust here