The United States is based on English government principles in several ways. These principles led the creation of the United States in July 1776.
The English citizens had enjoyed the freedoms that were included in the Magna Carta. This breakthrough allowed the citizens to have certain freedoms that were not given by the King prior like property rights, trial by jury and the beginnings of democratic principles. As English citizens the Americans thought they were to enjoy these freedoms also, but often times British attitudes were to the contrary.
An english philosopher by the name of John Locke had influenced many of the leaders of the colonies. Locke advocated a very powerful electorate that should demand that the government only exist to protect the freedoms of the people. He went as far to suggest that if the government that existed didn't protect these rights, that the people should get rid of that government.
So when you look at the turmoil of the time between the French and Indian War and 1776, you had a situation that had been created that was ripe for revolution. The freedoms that the American colonies thought they were to be given were in their opinion non existent. The leaders of the Revolution, such as Adams, Jefferson and Franklin demanded Independence.
The evolution of English government (and a parallel study of English History) shows a process by which political power became consolidated and wielded by one ruler. This was actually a necessary phase for England to become a country and a nation. Indeed, claiming the sanction of heaven through the political argument of the Divine Right of Kings served the executive powers of the king, or monarch, to justify his or her role in the Great Chain of Being. By the time of Medaeval England, the notion of "Divine Right" had been seriously questioned, and as embodied in the Magna Carta, had been curtailed. In effect, this document began the process of disseminating the absolute monarchy, and establishing a judicial and legislative branch of government separate from the executive. By the time of Renaissance England, the notion that not only was the monarch not absolute, but was also not above the law reflected the shift in power towards the legislative, specifically through the institution of Parliament. Democracy, where the people have say in the workings of government, became more prominent; Parliament became supreme over the monarchy. The notion that any "freeman" could have a vote and a political say reflected the trend towards individual freedom. America inherited this evolving British concept of government, and contributed the notion that if you didn't like the way you were governed, you could, and had a moral obligation to change it. The "parliaments" or legislative bodies of the colonies were sadly ignored and sidelined by the Parliament of London, and, by asserting the English notion of self-governance, broke away. In his Declaration, Thomas Jefferson refers to "our English Brethren" and, as colonists claiming the rights of Englishmen, asserts the notion of the governed to alter or abolish the government should they see fit to do so.
There will be many approaches to answering this question. Certainly, one way would be to suggest how American political thought was represented from English notions of the good. I think that one way this was present was in the American form of legislation. Drawing from the British bicameral system, the legislative branch consisting of an "upper" and "lower" manifestation (Senate and House of Representatives) draws from the British tradition of Lords and Commons. Another parallel from British law came from the Magna Carta and the English Bill of Rights, documents whose principles became an embedded part of the American political tradition. Rights and entitlements such as inalienable rights that must be safeguarded by government, as well as the notion of equality before and within the law, and the notion of habeas corpus (being aware of criminal charges) are elements that have become bulwarks of the American form of government. In terms of theoretical approaches to government, John Locke's English tradition of Enlightenment teachings were absorbed by the framers in the development of both the Declaration of Independence and the Constitution. The ideas of a social contract between rulers and their citizens as well as a sphere of freedom that cannot be vitiated are foundational teachings that were appropriated in the composition of American government.