There is no direct connection from Dunwich to Southwold. However, you can take the taxi to Blythburgh, Chapel Road then take the bus to Southwold, Kings Head. Alternatively, you can travel from Dunwich to Southwold in around 14 min.
From Dunwich taxi to Blythburgh, Chapel Road then bus to Southwold, Kings Head. 17 min £17. From Dunwich taxi to Southwold. 14 min £25. From Dunwich Uber to Southwold. 14 min £22. From Dunwich walk to Southwold. 1 h 41 min.