The society of the British colonies in North America was able to mature because it had a large number of colonists who were isolated from their mother country to a large degree.
To mature, a colonial society needs to be big. There need to be enough colonists to be able to create their own society that is independent of that of the mother country. If the society is small, it will depend on the mother country for all of the "finer things" in life. It will simply try to mimic the mother country. A larger society has enough people to make its own way.
The society also needs to be isolated to some degree. If it is easy to keep in close contact with the mother country, there will not be a feeling of separation from that country. It will be easy to continue to rely on the mother country for everything. This will hinder the maturation process in the society.
Because the English colonies were heavily populated and were distant from the mother country, they were able to mature.