At the time of the civil war only Virginia was a crown colony. Virginia originally stayed loyal to the House of Stuart but had to eventually signal loyalty to the new government. The New England colonies were almost all self governing. The end of war was more important as it returned the Stuart house to the crown and started the push to make all the colonies under direct crown rule.

If, by affect, you mean the influence that led the American colonies to their eventual destiny of seeking independence, then I do salute you for asking a great question. Since the English Civil War itself was fought between Parliamentarians and Royalists, a battle which eventually reallocated freedom and power to the legislative body, one can undoubtedly infer the eventual influence of the Civil War on the colonies. However, I'm looking at the broader picture here; it's ensuing affect, as an anecdote through history, on the Founding Fathers. Someone already mentioned how Virginia was the only crown colony; this is true. Much of the colonies were still at their embryonic stages. The response to this question, in my opinion, entails more than just mere facts. How so? Well, let us take into consideration Thomas Jefferson. Jefferson's ancestors from his mother's side, the Randolphs, were, ironically, major supporters of the king. William Randolph, his great grandfather, actually fought in some of the wars. This cost him almost everything he had. As a consequence -- and this is debated among historians -- this is what motivated him to consider emigrating to the colonies in 1672. At face value, such a fact is somewhat inconsequential; however, upon tying things together, one realizes that the development of vicissitudes would have been different had people of such ilk decided to remain in the British Isles. Reasons ranging from indentured servitude, to religious revivals (à la the Puritans) were among a long list of why people moved to the American colonies. Nonetheless, one must not rule out the eventual affect that this would have on subsequent generations. Once again, we go back to Thomas Jefferson; if one were to look at the Thomas Jefferson papers on a historic outline drafted by Jefferson the words "King Charles I is tried for treason by Parliament. Although he refuses to recognize the legitimacy of trying a king on such a charge...." appear. You can see how libertarian ideas are embedded thereunto. If this was written throughout the English Civil War, such a sentence would be expected of a Parliamentarian. Almost all the Founding Fathers were originally from the British Isles. This meant that recent history must have been substantial in forming their opinions with regards to the manner the Constitution was wrought. For example, in #69 of the Federalist Papers, Hamilton compares the president's powers to that of the King of England, he says:

"president's authority would be nominally the same with that of the King of Great Britain, but in substance much inferior to it. It would amount to nothing more than the supreme command and direction of the military and naval forces, as first general and admiral of the confederacy; while that of the British king extends to the declaring of war, and to the raising and regulating of fleets and armies; all which by the constitution under consideration would appertain to the Legislature."

For the sake of the discourse, let us put the Founding Fathers aside. What about a British politician? A Whig? The great Edmund Burke? This is what Burke had to say whilst writing about the French Revolution:

"In the famous law... called the Petition of Right, the parliament says to the king, 'Your subjects have inherited this freedom', claiming their franchises not on abstract principles "as the rights of men", but as the rights of Englishmen, and as a patrimony derived from their forefathers."

Even in the eyes of later English politicians, rights are derived from history. This idea is commonplace in England; I will not get into Precedent and its role in British law, yet its significance here is noteworthy. Since the Americans were more deferential in their revolution, adhering to their English roots, Burke was unceasing in his support. Where this ties in to your question: much of this discourse, at least Burke's arguments, were all being pontificated throughout the English Civil War and its preceding years. Not only was the power that the legislative body gained from this underrated civil war instrumental for those it directly affected, it also proved voluminous for thinkers it inspired such as John Locke, who used the occurrences of the English Civil War as the basis of his works -- which the American Founding Fathers, as I'm sure many of you know, heavily relied on. Ergo, this "affect" you were referring to is consequential to both the geniture of the colonies and their eventual destiny.