I have this excellent little poster that gives answers to questions like this. Probably still available online somewhere.
This indicates only Edmund Ironside and Lady Jane Grey as the "No coins" examples. I had an earlier version of the chart years ago, which also showed Sweyn Forkbeard as impossible, but it seems that has changed.
Edward VIII is possible if you go outside the UK. British West Africa and a few of the other Commonwealth Countries issued his coins in good numbers, though without his head, only his name.