In Scotland we have the TMSA, which should perhaps be TMaSAoS - Traditional Music and Song Association of Scotland: its national office is based in Edinburgh, but there are several branches throughout the country, largely run by volunteers, and each running their own events - festivals, concerts, competitions, ceilidhs, etc. The organisation also aims to preserve the various types of Scottish dance, though this does not feature in the title, and there are other organisations dedicated to this cause.
(As a by the way, the TMSA celebrates its 60th anniversary next year - big concert during Celtic Connections in Glasgow in January for starters!)
Not sure that the EFDSS has any branches outside of London?
The Irish Comhaltas movement also has branches in Scotland, a very long-running one in Glasgow, and a much more recently formed one in Edinburgh.