The US Constitution was intended to serve as a reform to existing British institutions, at least how they functioned in the colonies. Having a single written document containing the method of government was itself a reform, as in the UK then as now constitutional government is laid out across multiple laws. By the time of the American Revolution, Britain had established local assemblies in every colony with some level of home rule. It was disagreements over the extent of that home rule that led to the Stamp Act protests in the 1760s and then the decision to declare independence in 1776.
In getting rid of the Monarchy, they decided to have a strong executive who was indirectly elected (electors are still not bound to a candidate in the Constitution but their selection mechanisms in the states ensures the overwhelming majority vote as planned, and no election has been thrown by rogue electors). eta: Most colonies had a Royal Governor, appointed by the Crown, as chief executive with an elected assembly representing land owners. The Senate was originally appointed by the states according to their own various methods, either by the state legislatures or the Governors of states. It was intended to have a similar function to the House of Lords, which had more power in British government at the time than it does now. The primary function being to slow down democratic movements.
As in the UK, voting in the colonies was based on paying a poll tax, meaning you had property or business interests. After 1800 states changed to "universal suffrage" which allowed any free male over 21 to vote. In the colonies women who owned property (usually widows holding property until their minor sons came of age or they remarried) could vote, as could free blacks if they paid poll taxes. The new laws allowed more men to vote but put race and sex restrictions in place.
There are specific issues that are addressed in the US Constitution that would later happen in the UK. One example is the requirement for a ten-year census. Many seats in Parliament were based on medieval population, and by 1776 the industrial revolution had caused cities to grow while rural districts had lost population. As the colonies did not exist when districts were formed, there were no North American members of Parliament, but the same could be said of several large cities in England as well. That made "no taxation without representation" a rallying cry in the colonies (they did not oppose taxes, but held that colonists could only be taxed by colonial assemblies, while port duties were the prerogative of the Crown through Parliament in Westminster). Shortly after 1800 the UK began taking a 10-year census as well, and districts eventually came to match population.
So in may ways our constitution was quite modern in 1789, it has not kept up with modern needs. We are stuck with an Enlightenment document that does not even mention political parties and has outdated remnants of our slaveholding past. Because the United Kingdom has a series of laws that lay out government, they have been able to adjust their institutions in a way that is now impossible in the US.
