How can I scale curved surfaces radius but leave its width alone? I have a curved set of faces, made by creating 2 circles, joining the objects and then joining the verts I needed while removing the others.

Unfortunately the resulting object has the wrong radius. See pic 

Is there any way that I can scale it so that the radius changes, but the width of the faces remains the same? In effect what I want to do is tighten the curve so that lowest edge (in the top ortho view) is much closer to the top, as indicated by the yellow arrow.
Yes, so long as you know the center of the radius.

Place your cursor at the center of the circle.  Change to cursor pivot with . key.  Select your mesh.  Use the push/pull operator, available from spacebar search, or from the mesh/transform menu.  Move your mouse until you're happy, then LMB confirm.