I live in Garsington and have a Radford in my family. I have not found a connection to the Garsington Radfords as yet but I have not tried too hard. My Radfords come from Stanton St John or Albury and Waterstock (these are all down the road from Garsington.
Stephen Radford b 1796 married Mary Butler they moved from Stanton St John to Charlton on Otmoor (not too far away) all in oxfordshire.
Please look at: faces.oxfordshire.org.uk where there are some pictures of Stephen Radford and Catherine Radford. They are all too close to not be related somehow.
Thomas Radford married Sarah Mortimer.
Let me know what you think.