I'm not for sure if England benefited from Rhode Island per se. However, Roger Williams was a separatist who came from England. He had different views than the Puritans in Massachusetts and was then exiled. He moved to what is now "Rhode Island" with some of his followers/ peers and founded the city of Providence. He began witnessing to the Native Americans there.
Later, a war broke out between some in Massachusetts and some Native Americans (The Pequot War). The people of Massachusetts asked Williams for aid, and he used his relationship with some of the Native American tribes to dissuade them from joining in the war. These Native Americans joined the alliance with the English and helped in winning that war.
roger williams benefited from founding rhode island because he could express his views there, something he could not do in england, and at least 2 other settlements in the new world.
as far as england benefiting, the only thing i could think of is that they could rid themselves of people who did not want to be under the thumb of the ruling 'religious' caste.
since farming was difficult in RI, shipbuilding, whaling and fishing were the main ways of making money.
they would build and sell ships to england, and probably sold/traded whale blubber, and possibly salt preserved fish to/with england.