BBC Radio 4 Website

The show is called "Border Ballads"
14:45 (2:45PM) in the UK/9:45AM Mudcat time.
They have some shows archived, but this doesn't currently seem to be one of them, and isn't in their "A-Z" list of shows.

From their "What's On" page:
History of the border ballads. Michael Tickell discusses The Battle Of Otterburn, which relates how Harry Hotspur, Duke of Northumberland, took revenge on James Douglas in 1388. Then News.