I've just got a Radio Times for the week before Christmas (16th-22nd issue, Doctor Who on the cover) and there was an article about a new production of Sir Gawain and the Green Knight. Not the Tolkien version, but a new one by Simon Armitage (should be good, he's a great guy), and narrated by Ian McKellen.
This will be on Radio 4 at 2:15pm on Thursday 21st, but should also be available afterwards to all via the 'listen again' web feature.
Here.
There's a bit about Tolkien in the Radio Times article too.