I mean large scale wars, so less defined conflicts like The Troubles (Northern Ireland) dont count. Further questions:
If you include countries that have English as an official language, you're looking at the Kargil War, also known as the Third Indo-Pakistani War, in 1999. (I hope just mentioning it doesn't violate 20 year rule) That said, one could credibly argue that you should not count India and Pakistan as English-Speaking, official language or not.
I suppose with the more narrow take the Irish War of Independence 1919-1921 is your answer.
[Here is a rough-guide to one system linguists use to classify which countries are English speaking] (http://www.fb10.uni-bremen.de/anglistik/linguistik/images/lehrerausbildung500.gif) for the purposes of your question I'd narrow it to the inner circle (United Kingdom, Ireland, the United States, Canada, Australia and New Zealand)