After a lot of research (and ruling out buying my own brick cutting machine!) I decided that running a small diamond wheel at a slowish speed on my Dremel was the way to go. The glass needs to be kept wet so of course I get wet too; I've invested in a proper safety visor to keep the wet ground glass spray away from my face. And at the moment I do the cutting outside!
As you can see on the left, the initial cut is jagged and not very safe so I then spend some time polishing the edge smooth. The one on the right is nearly done...
Next step will be to mask off my design and get sandblasting.
And in the best Blue Peter tradition, here's one I made earlier, now available in my Etsy shop.