I'm not English -> I didn't grow up with fairy cakes. Anyway, I don't like cakey cakes.
I make carrot cake, courgette lemon, beetroot chocolate, banana cake, pear cake, orange and pumpkin cake. They're all more wholesome and moist than fairy cakes, but not so light.
phdlife, you kinda need a coffee grinder, maybe you could do it with a mortar and pestle I guess [skeptical]. But one egg = one tablespoon of fresh-ground linseed + 2 tablespoons of water. This does the same binding and moistening things as an egg, but it doesn't rise like an egg.
I think fruit/veg cakes can be relatively low-gi. I always include fruit/veg/nuts in mine, the nuts deffo lower the GI. I use brown sugar in place of white (doubt this makes much difference) and substitute wholemeal flour for half or more of the white stuff. The sugar and the white flour is bad for GI, the fibre from the fruit/veg, and the protein/fat from the nuts, lower the GI. Wholemeal flour helps, too, of course.