This poem was written after what was known as the Peterloo Massacre which occurred in Manchester in 1819. It was four years after the end of the Napoleonic Wars and England had fallen into recession, and the north of the country had been hit particularly hard. In response to this the working class began to stage a series of protests with culminated in Peterloo, and the response to these protests was a cavalry charged by the British army which left 15 dead and 700 wounded.
Shelley writes in a rather apocalyptic style in his response to the massacre and uses the imagery of the four horsemen of the book of Revelation, though he actually names three of the horsemen, with the forth horseman being named Anarchy. I suspected that this forth horseman related to the English government. I also suspect that it suggests that where the government is concerned there is no law that binds them and as such the country lives in a state of anarchy. While there is law that restricts the actions of those who live under it, the higher one goes, the less the law imposes restrictions on them. Mind you, the cavalrymen would have been just as much under the law as the people whom they charged.
This is not the only text in which Shelley explores the theme of the lawlessness of the government as he also explores it in The Cenci, where the antagonist rapes his daughter and gets away with it, but when the daughter and her brothers then seek revenge against him for his crime they are captured, tried, and executed for their participation in the deed. With regards to the Peterloo Massacre it is clear that the cavalry may have, on one hand, been attempting to keep the peace, but more likely than not it was acting to protect the interests of the masters of the land.
What Shelley laments a lot during his writing is the failure of the French revolution. Granted, Shelley was only a child at the height of the revolution, and would have entered his adult life during the reign of Napoleon, however it is not so much the failure of the revolution that is important, it is the ideas that it generated. Once the idea of freedom for the masses came to the fore in France, it began to filter throughout Europe, and even across the channel to England. In 1795 England was practically on the verge of revolution herself.
One particular line in the poem demonstrates the lawlessness of the government when Anarchy says 'I am God, King, and Law' indicating that all law stems from the government, but with government being Anarchy, there is no law because something cannot come out of nothing. To Shelley the government is illegitimate, and as such the law it creates is also illegitimate because there is nothing, other than brute force, that gives it legitimacy. Being an atheist himself, Shelley no doubt completely rejects the divine right of Kings.