England had recently been at war with France when Jonathan Swift wrote the novel, in the War of the Spanish Succession (1701-1714).
The Tramecksans, or High Heel Wearers, represented the English Tories. The Slamecksans, or Low Heel Wearers, were the Whigs.
High and Low are in reference to the fact that though both Tories and Whigs were Anglicans - members of the Church of England - the Tories tended to be High Church, or more nearly Catholic, and the Whigs tended to be Low Church, or more liberally Protestant.
The prince who cut his finger is usually taken to represent Henry VIII, who "cut his finger" on Catholic doctrine when he sought a divorce from his queen. The pope's refusal to grant the divorce led Henry to found the Anglican Church.
The "injury" was still being disputed at the time Swift wrote Gulliver's Travels.
Gulliver's victory was accomplished by a naval maneuver. This reflects the Tory attitude during the War of the Spanish Succession. The Tories favoured naval action as being less expensive and less dangerous than land action. It was the Tories' view (and Swift's) that this was the decisive blow that won the war and ensured British dominion over Europe and the world.
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This fire-extinguishing incident symbolizes the Treaty of Utrecht, by which the Tories "put out the fire" of war. Gulliver fell into disfavor through his actions, just as the Tories did. In the Tory view, the secret treaty was necessary to avert total disaster. It did indeed stop the war but also brought shame, political destruction and charges of treason.
Swift's utopian notions derive from Plato's Republic; much of the Republic is modeled on the Spartan ideal way of life, which was incredibly austere.
As soon as George I came to power, Atterbury fell from favor. In 1723, he was arrested for complicity in a Jacobite plot to replace George I with the Pretender James. He was convicted and forced into exile.