Actually, this happened a fair amount in real life. Think of the "English Army" as excess English/Norman nobles sent out to conquer new lands or defend the English core area from the surrounding Celtic peoples. Each of these guys was given great autonomy, almost viceregal power, due to the lack of support and communications with the Crown. As a result, they tended to want to become independent, establish their own kingdoms, etc., and they came to see each other as more kindred spirits than their nominal overlords back in the English core area. And thus ther were often wars between these "Marcher Lords" and the Crown, and having the "Kingdom of England" at war with the "English Army" is therefore realistic.
For example, check out the history of the De Clare family who built Caerphilly Castle in the "English Army" partof Wales. That castle was way ahead of its time in terms of conentric walls, masive moats, etc., and was built by a nobleman, not the King. Sure, it was a frontier fort, but it was rather overkill for what he Welsh had to ofer. It was mostly built to defy the Crown.