You are bit further North than me, Stu, but I suspect that you may be in a similar position to me in that the bark on Birch doesn't really grow thick enough to use for watertight containers. I believe that it is thicker further North (e.g. top end of Scotland and Scandinavia) because it grows thicker to help insulate the tree during the colder winters.
In my experience, long fallen trees do not provide good bark for container work - the bark is too old, dry and crispy for anything other than firelighting. What you really want is a tree that has fallen not too long ago. In this case, the bark (certainly in Southern England) is only maybe 1mm or so thick. I run the point of my knife in a straight line in the direction of the trunk (i.e. vertically if the tree were still standing) and it is really obvious when you have cut through the usable bark as it does begin to separate from the wood. You then need to cut a couple of 'circles' around the trunk and then start gently to ease the bark away from the trunk. It's best to use something relatively soft to do this (e.g. a stick sharpened into a chisel shape) - I've used my knife before and it scratches the bark.
If the bark comes away cleanly and is 'leathery' then it is fairly good - it's difficult to describe, but when you've got a good bit of bark, you'll know. The inner surface is a nice shiny brown colour.
You will probably find that the bark has lots of small horizontal slits in it (which make it useless for watertight containers unless you plug these with pine resin or something similar). However, you can make containers for loose items (nuts /berries) or split the bark into strips for woven baskets. You will also probably find that there are quite a number of knobbly bits (I think where lower branches were growing when the tree was young) which limit the size of the sheet that you can obtain from the tree.
Hope this helps.
Geoff