On high voltage transmission towers (pylons) there are sausage like
things, perhaps 200mm long and 50mm wide hanging below each cable a
short distance from the connection of pylon insulator and cable. Why
are they there?

I haven't found any references, but I believe they're there to damp
vibrations in the cable.  You can see the same things on cables in
suspension bridges.

Ian G.

They are insulators. They provide the space between the high voltage
cable and the metal support on the pylon.  They have to have that
distance or the electricity could jump the gap (like lightening).  The
higher the voltage - the bigger the gap.

Further - they are made out of glass or ceramic material. They look
like springs because they are like a concertina in construction.  This
gives a larger surface area between the support and the high voltage
cable - especially important in the wet.