Ok, guys, I know this is a folk forum, but sometimes I think that people here are a bit unrealistic about the reach of the genre, and the artists who perform in it. There is no way that the average British 16 year old will have heard of Alasdair Roberts, and although I stand to be corrected I suspect that there is no way that the average American 16 year old will have heard of Anais Mitchell. Folk is a niche, and not one that teenagers in general inhabit. The original post asks for artists who charted this century, and those operating in the folk niche won't have. Nic Jones never even charted for goodness sake. I don't think that Bert Jansch did. Fairport convention got to number 21 with a French translation of a Bob Dylan song. Steeleye Span were a bit of an exception, they had two chart hits, one a medieval carol, and the other a song from the 1820s (so semi-traditional).

The OP asked for 21st century chart artists who had covered traditional songs. I can still only think of Ed Sheeran. Sure, 50 years ago there was Bob Dylan, and sure, he still records, but the only traditional stuff on any of his 21st century albums is Christmas Carols.