If you're looking for a podcast about running may I recommend Running and Life (http://runningandlife.co.uk). It's a podcast about running that's for runners of all backgrounds and abilities.
Monthly, 30 mins long - it's NOT a podcast where you get preached at about the 'right' or 'wrong' way to run, just one that features a mix of short interviews with people doing amazing running challenges, or interviews with people from organisations like UK Anti Doping and UKA. Plus race reviews, reviews on running books and sometimes just a bit of mucking around!
if you're looking for podcasts on running, may i suggest Running and Life (http://runningandlife.co.uk). Interviews with people doing amazing things in the world of running. This month: Andy McMenemy on his attempt to set a world record of 66 ultras over 66 consecutive days in "Challenge 66", and Mike Buss who would like to set a world record..........for running while on fire from head to toe (i kid you not!).
i echo what PhilPub says. i work in Greenwich and i'm lucky enough to be able to choose between Greenwich Park, Blackheath, or up and down the Thames pathway (not so green, lots of tourists, but worth a jog every now and again....)
Oxleas Woods is also great but if you want to keep going much further south then just south of Bexley there are too many green spaces to mention them all, though Joyden's Wood is ace (if hilly!)