Well, it seems this is turning into a cookery blog! It turned out that the second half of the Accidental Brownies was so burned that it was not worth eating.
Attempt 2 (using more baking powder, a little bit of Xanthan Gum, more oil, less water, and some Stork - as shortening is impossible to get hold of round these parts) was made Wednesday, and was slightly more successful. The cake rose massively at the edges, overspilling the tins, but failed to rise in the middle. It also turned out to be rather greasy (oil needs to be replaced with water, I'd guess). It has less of a tendency to fall apart than did the last attempt, and now it's iced it doesn't taste half-bad. Although it's not the sponge I was going for. I've ordered some Allergycare Egg Replacer from www.goodnessdirect.co.uk; I'll make another stab at the sponge once that arrives.