There is a very great deal of continuity between the British and colonial American political processes and the political system that we have in the United States today. There have, of course, been changes, but the basics remain very much the same.
We think that the British government was a tyrannical monarchy, but it was not. The Parliament already had a great deal of power, particularly after the Glorious Revolution in 1688. Many people (though not the colonists) were able to vote for members of the House of Commons. In the colonies, people also typically got to vote for the lower houses of colonial assemblies. In other words, representative government was very much in existence even back then.
Of course, there are major differences. The British Parliament had an unelected House of Lords. The American colonial assemblies had governors appointed by the British government and unelected upper houses. Today, we have upper and lower houses, but both are directly elected. Today, all men and all women can vote. Back then, no women could vote and many men could not vote either if they lacked property.
However, the basic idea of representative government comes to us from the British and from the colonies. This is the foundation of our system.