Nope. I though barm is what you northerners call a bread roll. So a barn cake would be a bread roll cake?
There is no such thing as a bread roll unless you count the old round Milk Loaf in which case it would be a fair name.
Cake doesn't just refer to a confection - it's more to do with the shape. You can have cakes of watercolour paint or cakes of soap, for example. In Middle English the word exclusively meant a type of bread, a flattish shape different to a loaf. They couldn't sweeten it like today, apart from spread a little honey on it perhaps, and it bore no resemblance to what we usually think of as cake. So traditionally the word meant bread, it has evolved but still survives in barm-cake. Barm is the foam off fermenting beer and is used to leaven the bread.
Hmm where I’m from a cake is a cake. And bread is bread. We just have one word for bread in the shape of a cake, it’s called a roll.
And French too hence Marie Antoinette saying "let them eat cake. Not quite as stupid as it first sounds but still a poor show.
You're entitled to call them whatever you like - as is everyone else. I'm just pointing out that barm-cake is a traditional and perfectly legitimate name, and not as "weird" as you seem to think.