Then hubby walked passed and said 'why don't you just mold the bark around the pot, tie it on, and leave it to dry in that shape before you try and stick it'. I think I probably looked like a goldfish for a moment while I digested his comment; it is in fact really obvious once someone points it out, and it works like a dream.
There are a few fallen Birch in one of the woods where we walk our dog, so I had been thinking about trying this for a while. Note: Please don't remove bark from living trees. Removing even relatively small pieces of bark can result in the death of the tree.
With my new found knowledge of working with Birch Bark I would suggest if you do pick some up, that you immediately roll it with the outer face of the bark on the outside and secure it, as it will naturally curl the other way if left to its own devices as it dries, making it much harder to work with.