What was the monarchy and government like in 19th century London?

The nineteenth century was a period of dramatic change in England. Legally, England is described as a constitutional monarchy, with the monarch having powers limited by Parliament. The nineteenth century was a period of great change though in how Parliament was elected, the relative powers of the two houses of Parliament, and the relationship of the monarchy to Parliament. 
There were four monarchs during this period: 

GEORGE III 1760 - 1820: Due to his increasingly erratic behavior due to mental illness, his son ruled as Prince Regent from 1811-1820. 
GEORGE IV 1820 - 1830: Note that he had been Prince Regent from 1811-1820 and was a quite colorful character.
WILLIAM IV 1830 - 1837: Brother to George IV.  
VICTORIA 1837 - 1901: Giving her name to the "Victorian" period, Queen Victoria was one of the longest reigning monarchs in English history and presided over a period of great prosperity.

The three Reform Bills of 1832, 1867, and 1884 gradually expanded voting rights from the wealthy to most adult males. The House of Commons became increasingly powerful compared to the upper house. The civil service expanded, with the government beginning to fund and manage such things as public schools, poor relief, marriages, census taking, and citizenship records that had earlier been the responsibility of the church. 
London itself had no municipal government, but rather a miscellaneous collection of parishes and vestries and special-purpose organizations such as the Metropolitan Police (established by Prime Minister Robert Peel, and thus called "bobbies" or "peelers").