The word you're looking for is "yeoman", btw. Peasantry is a larger concept which also includes serfs, but the yeoman farmer was exactly what you're describing.

The word you're looking for is "yeoman", btw. Peasantry is a larger concept which also includes serfs, but the yeoman farmer was exactly what you're describing. "Rich" might be pushing it in an Anglo context, but land owning and powerful, though not in comparison to the aristocracy.