If you want lineage then there is no umbrella term at all that will cover the lineage of British morris dancing other than err, British morris dancing.
I still don't understand your necessity for grouping them in any form? For the record I go by region/continent for my own organisation to make finding what I want in my library but if I want a historical perspective then its far more specific, see again morris dancing, it has little to do with white man + acoustic guitar of the mid 1900s for example.
This and /trad back in the day were 'traditional folk' for everything because when there are only 10 people interested and all with differing tastes (Hamp and I didn't like anything the same) then you need the broadest topic to get the discussion flowing.
and this is the great thing about mmusikchan, so few come here so threads last years!