What was the impact of the English Bill of Rights on United States history?

Simply put, the most important impact was the first 10 amendments. These define clearly what the individual citizen has the right to expect from the laws of the land and governments in general.

The founding fathers were very concerned about those individual rights. They really didn't want to give the federal government any more than was needed to function. An interesting side view of the constitution which is used today is that the founding fathers tried the articles of confederation first (for 8 years). Finally they gave up on that idea and wrote what we have now.