How was Britain divided into the rich class and the poor class in the second half of the 19th century?
First, it is important to note that many historians do not think that British society was divided into rich and poor classes in the second half of the 19th century. For example, one textbook that I have used when teaching World History says (Source: Kagan, et. al., The Western Heritage 8th Edition, p. 818)
The sixty years before World War I were the age of the middle classes.
This means that historians do not really see this as a time when society was neatly divided into rich and poor.
The major factor that caused society to divide into rich and poor (and middle classes) was the second phase of the Industrial Revolution. This second phase, which lasted for most of the second half of the 1800s, was dominated by the production of things like steel, chemicals, and oil. This phase of the Industrial Revolution led to the creation of large companies. The owners of these companies became very rich. The masses of people who worked in unskilled jobs in the companies remained poor. This is the division of society between rich and poor. However, there was also a middle class that started to arise as these companies needed white collar workers such as managers. The middle class also consisted of shopkeepers and professionals.
Thus, historians do not really see this time period as one in which people were either rich or poor. However, there were certainly divisions between the rich and the poor which were caused by the increasing industrialization of society and the creation of large companies that went with it.