I had thought that shaving the back of your arm with a plane blade was an urban myth, perpetuated by the Old Woodworkers to make us new guys feel perpetually inadequate.
However, in search of sharpness, I bought some high carbon plane blades from Hock Tools and a set of Ice Bear Waterstones from Axminster. (Nice fast delivery on both counts)
So I spent the time flattening the back of the blade, then honing the front till I found the burr, then removing the burr.
And there you go. It lifted a few hairs from the back of my arm, not quite up to Gillette's standard, but sharper than anything I've managed previously.
I am converted. My old wet and dry paper collection will now be reserved for flattening the wetstones. I've already ordered a course 220 grit wetstone to do the back of the cheaper blades, which have far move visible machine marks.