That picture looks exactly like the two dozen caterpillars I have just picked off my 'Betula utilis jacquemontii Doorenbos'. They had already cleaned all the leaves off one branch and had moved onto the next. They are now wandering around in the tray of my bird feeder!
As my tree is only 3 years old I was concerned that just a small group of these could strip it bare in no time at all so I will be out to inspect the tree again tomorrow.
btw - the leaf in the photo looks just like my tree and as far as I am aware this Betula is a "Silver Birch"
Also found a photo on Wiki under Sawfly.