Here's an interesting article in 'Musical Traditions' about the Millen familiy of Kent - scroll down to find it. Like the Coppers, they have a current family tradition of singing in harmony and the article briefly explores its origins. It mentions the Batt Brothers of Kent, too, who also sang in harmony.

I heartily endorse the recommendation of The Claque. Here they are on YouTube at Cheltenham Folk Festival 2009. The sound is not very good quality, but it gives an idea of their distinctive style.

Valmai (Lewes)