Yes, but Hutton doesn't sing the song in the programme ... there are no archival recordings of him.
The drama is merging fact (there was a Richard Hutton in Goathland who sang the song to Cecil Sharp), and fiction (what the drama is all about). For example: ....

"Tom refuses to be drawn on the significance of Scarborough Fair, but admits that the singer of the song, Richard Hutton, was his wife Dorothea's grandfather."

And yes, the VWML was consulted about this. The image of the field notes will have come from Clare College Cambridge, though it can be seen in The Full English online digital archive. www.vwml.org

Derek