They're in the aphid family. Now aphids are susceptible to soapy water, because they breathe through their skin and you basically suffocate them by locking their breathing apparatus. However, woolly aphids are a lot trickier, because the white stuff you see is a waxy excretion they use to protect themselves from predators - it also protects them from soapy mixtures. I would spray them with a bee friendly preparation of some alcohol based stuff, like surgical spirits, or even good old meths. That will dissolve their waxy coating and leave them vulnerable. If that doesn't actually kill them, then after a treatment with a spirit based spray, give them a second soaking of good old soapy stuff. You can buy insecticide soap spray, but a squirt of washing up liquid mixed with water in a spray works just as well.
They're also hard to get rid of because they're 'perennial'! They overwinter so a colony doesn't just last for one season and then dies. They're not so tough as to get the better of you though Spuds, just a little more difficult than their cousins. They DO like apple trees, the clue is in their name - "Apple Woolly Aphids"
: my apple tree ( 398 )