There is a recent (2017) edited volume that may help you: Quaker, Business and Industry by Steve Angell, Pink Dandelion and Paul Anderson, Friends Association for Higher Education Quakers in the Disciplines Series, Vol. 4, FAHE: Longmeadow Ma. Amazon has the introduction as a preview, which summarizes various theories. (Yes, his name really is Pink Dandelion. He changed it as a young punk in the early 80s.... and is one of the most important Quaker theorists today.)

The conventional explanation among Quaker Historians was that it is at least in part due to that fact that as religious non-conformists, Quakers were denied entrance into Universities and thus into other professions. This probably is a factor, but there is also a link in the US, where Quakers had full rights. They also had a reputation for honesty and hard work. One contemporary argument is that the pressure to marry within the faith, combined with wider social pressure to marry within one's class, meant that those who were successful consolidated wealth with a few Quaker families. Despite an emphasis on simplicity, business tended to be seen by Friends as a worthy enterprise, especially when combined with philanthropy.

In any case, like most cultural phenomena, there is not any one single answer and a variety of factors at play.

The Religious Society of Friends (proper name of the Quakers) pursued a business model centred around their religious principles and conscience before profit: i.e. in plain-speaking, egalitarianism, concern for the planet etc. Actually, they were very ahead of their time. Thus Quaker-owned businesses gained a reputation for being fair and trustworthy and became very successful.