Denham has a small but important role as the friend and benefactor who helps Franklin out during his first trip to England. He impresses Franklin with his Quaker sensibilities when they meet on Franklin's first voyage to England. During this stay in England, Denham almost acts as an externalized version of Franklin's consciousness, giving him advice and helping him out. For example, he reveals his kindness and honesty by helping Franklin figure out that Governor Keith has broken his promises and abandoned him. Denham's also the voice of reason in this moment, as he's the one who tells Franklin to get off his butt and find a job. He fills this role later, too, when he tells Franklin to stop wasting money and start saving so he can return to America. Denham even offers Franklin a job if he returns to America with him.
During Franklin's description of Denham's backstory, we learn that honor and integrity is really what defines him. The Englishman has some bad debt in his past, just like lots of other people. He's unusual, though, in that after going to the American colonies to start over he returns to the people he owed (in Bristol) and makes it all up to them. Through this act of repaying his debts, Denham embodies financial virtue. While he's kind to Franklin to begin with, Denham also becomes permanently loyal to him after Franklin helps him thwart a plot against one of his friends, Andrew Hamilton.
Besides Franklin, he's one of the most principled characters in the text. Structurally, then, he serves as an emblem of what an honorable man can be or should aspire to; despite the fact that he, too, has "errata" in his past, Denham's able to overcome them.