How are the king and the duke able to convince the townspeople that they are Harvey and William, Peter Wilks' brothers?
To me, there are two reasons that the "king and duke" are able to fool the townspeople. One reason has to do with the two men's luck and cleverness. The other has to do with the ignorance of the people in the town.
First, the two crooks are lucky enough to meet the young man who tells them about the death of Peter Wilks. They are also clever enough to see an opportunity and to pump the young man for a whole bunch of information that will allow them to pass as Wilks's brothers.
Once they get to the town, they also have to rely on the ignorance of the people. The people do not know what people form England would act or sound like and so they are easily taken in by the king and duke's act.