BBC Category : Folk
Heres the BBC page which gives links to their current Weekly/Monthly/Seasonal radio programmes and a few one-offs.
Mostly regular shows (likely to change) and some old series which might episodes available
Ambell i Gân (Cymru)
A' Mire ri Mòir (Nan Gàidheal)
Caithream Ciùil (Nan Gàidhea
Catgut and Ivory (Scotland)
Celtic Heartbeat (Wales)
Claire and Friends (Scotland\Shetland)
Crùnluath (Nan Gàidheal)
Dashing White Farmer (Scotland\Orkney)
Fae Hameaboot (Scotland)
Folk Club with Lynette Fay (Ulster)
Georgia Ruth (Cymru)
* Iain Anderson (r2)
Music Planet (r3)
Oota Da Cans (winter only) (Scotland)
Pipeline (Scotland)
Pipes and Drums (Scotland)
The Piping Season (Scotland)
Piping Sounds (Scotland)
Roddy Hart (Scotland)
Saltfish Sessions (Scotland\Orkney)
Sruth na Maoile (Nan Gàidheal 2019)
Take the Floor - Gary Innes (Scotland)
The Folk Show With Mark Radcliffe (r2)
Tim Walker's Folk (Lincolnshire)
Tiompan (Nan Gàidheal)
Trad Ar Fad! (Ulster)
Travelling Folk (Scotland)
What's the Craic - Irish music scene (Scotland\Orkney)

- NB open the link in a browser; don't just click the link or it will try to open your 'Sounds' app and this doesn't provide the same information as the web page -
www.bbc.co.uk/sounds/category/music-folk?sort=title

*One regular programme missing from the page above :
Iain Anderson (country, folk, blues and soul) r2
www.bbc.co.uk/programmes/b0074hkv/episodes/player