I've never been there, sorry. The closest to there that I've eaten something was at Dingle Hill Tearooms. They do decent vegan stuff--simple café food but not bad at all. I doubt you want to ride to Dunwich in this weather, though. :)
Not in Southwold but near it. The Unruly Pig has a very meaty menu in general, but enough well marked vegan dishes (and drinks) that you can order well.
Any recommendations for vegan friendly pubs / restaurants in Southwold?