Frank Erskine wrote:

What do they call the type of handles that were fitted to, for
example, old Dansette record players and the like?
If you remember they consisted of a strip of spring steel, covered
with leather or rexine, with longitudinal slots at either end, and
there was a metal cap which was fastened on by a screw which went
through the slots.

Moreover, does anyone know of a source of these? I only need one, to
fit on fixing centres of about 6¼".

Strap Handle

http://www.maplin.co.uk/strap-handle-33254

Perhaps more elegant ones exist?