When it comes to the English music tradition don't forget that for most people Church music and folk music were two sides of the same coin. The church musicians were the barn dance band. Look at the complexity of some of the West gallery music and then you will realise that there was plenty of harmony singing around available to all.
Am I unusual in experiencing a tune as a chord sequence around a melody, whether or not the chords are actually being played? For me the harmonies are there ready to be sung, and probably nearer my register!