After chasing through my stitch books up came Edith Johns' Zigzag Petal stitch - a two way stem stitch with the addition of a detached chain in the middle of each stitch.
Not a particularly well executed example - I definitely need to practise to get the stitches more even. However this gives the general idea of the stitch. I usually work stem stitch without a hoop or frame and feel my control is good - however some tautness of the fabric might be a good idea for the chain stitch - something for me to remember in the future.

