I've been trying to find this pattern to share for ages. It is from a Sirdar "Bazaar" book from eons ago. The price was 2shillings and 6pence so that gives you some idea of how long ago!
Anyway, the scarf.
The finished fabric looks like tubular stocking stitch knitting that has been joined at the ends.
Cast on double the number of stitches you need for the finished width. So, this means an even number of stitches.
For every row, *Knit 1, bring wool to front, slip one stitch purlwise, take wool to back,*. Repeat this right along the row.
Work length of scarf required then cast off by working two stitches together all across row (if I remember rightly you then do a normal cast off with remaining stitches)
Yes I know it sounds odd but it works. (Ithink!)