The name is now restricted to Lancashire and parts of Cumbria and Yorkshire where filled bread rolls are customarily referred to as 'barms', but seems to have formerly been more widespread as the name occurs in advertisements and news reports in Derbyshire and Northumberland. See: Bread Names
Brown Barm Cakes, 2013
Barm is an old term for 'yeast' and there is some evidence that barm cakes were formerly leavened with the yeast-rich froth from brewing beer.