It's hard to tell but the tree is possibly one of the wild prunus - bullace, cherry plum, damson, that sort of thing.
It has been badly attacked but it's the price we're paying for a mild winter - many aphids survived the winter and made a head start with their breeding programme early on!
As I said, I think the best thing you can do for the tree is to encourage the birds to do the job for you, and hope for a few good sharp frosts next winter to knock the aphids back.
I think that with the honeysuckle I would pinch out all the badly affected growing tips. That number of aphids will have damaged them so you won't get good flowers. If you pinch out the growing tips the honeysuckle will grow sideshoots which will hopefully flower later this summer - and even if they don't flower this year, you'll have a bushier plant which will be good.
Again, resist using insecticides as they kill the good critters as well as the bad, and this is why we get the big inbalances. It may take a couple of years to get things in balance in your garden, but we've been here three years this coming August, and I've just been watching a large brood of newly fledged bluetits hoovering up aphids from my honeysuckle - they do the job and they're such fun to watch.