In Shelley's poem, "England in 1819," the historical allusion he makes is to the "old, mad, blind, despised, dying king." This would refer to George III. Though it seems that George was well-loved by the people early on in his rule, as he got older, he was thought to be mad.
(In 1966, however, psychiatrist Ida MacAlpine and her son Richard presented the theory that George suffered from porphyria which may not only have accounted for his bizarre, "insane" behaviors and physical ailments, but perhaps also those of his ancestors Mary Queen of Scots and her son, James I of England, who also suffered from some of the same physical maladies of this disease.)
However, at the time George was believed to be mad. He recovered after his first serious bout with the disease for 12 years, but then it returned; George would never recover. Though he remembered he was king, he did not recognize his wife. His son George was named Regent at this point. In his eighties, having spent 10 years shut away in Windsor Castle, George III the third lapsed into a coma, never to regain consciousness.
The historical allusion continues with mention of the princes who ruled in George III's stead. They governed without regard to the well-being of England's populace. Their behavior seems to be connected to the religious allusion below.
The religious allusion refers to the monarchy's attitude towards God while ruling England. The laws pushed the envelope contrary to the laws of the Bible, or outright broke those laws. The country was led by those who had turned their backs on Christ's teachings, and with no regard to God's laws; the Bible, which should have guided the leaders of the day, remained closed.
The mythical allusion in this sonnet refers in the last rhyming couplet that speaks with hopeful expectation of a "Phantom," a hero who would appear and bring peace to the country's tempestuous existence, releasing the people from the terrible control of their leaders. (Queen Victoria would be the next monarch, leading the country strongly into the 20th Century, ruling for 63 years, though this poem was written before her reign began.) It would seem that Shelley's wish came true, though the "hero" was, in fact, a "heroine."