I've archived this in downloadable form on Soundcloud for anyone who missed the original broadcast or who wasn't able to hear it on iPlayer. It's here:

Martin Carthy on Mike Harding 11 May 2011

In addition, I've also archived a handful of other radio programmes featuring Carthy (as well as a couple of interviews recorded live at Cambridge Folk Festival):

Folkweave: Live at Cambridge Folk Festival 1977 (BBC 1978)
Imagined Village Interview: Cambridge Folk Festival 2008
Topic Records interview: Cambridge Folk Festival 2009
Lost Albums: Bright Phoebus (2007)
Once In A Blue Moon: The songs of Lal Waterson (2010)
Imagined Village live at Cambridge Folk Festival 2010
Norma Waterson: "Gift" interview July 2010
Martin Carthy: WNYC Public Radio interview 2005
Concerning Franklin and his Gallant Crew (2010)
Three tracks from a 1983 John Peel session

I have a few other programmes on tape, mostly from the late 80s/early 90s, that I'm going to work on transferring to digital format over the next couple of months. When I do they'll appear on the "On Air" section my website so keep a look out.