Salkeld Mill is an incredibly quaint little tea room that has vegetarian menu and one or two vegan options (soup or stew special when I went). The food is very rustic and homely. The bread is especially nice. They have nice looking vegetarian cakes but as far as I know only vegan ice cream. They sell many different types of flour from the mill there.
Cons: Limited vegan options, Vegan options not always labelled, Sometimes busy, slightly chaotic service