Our drain runs from our garden to next door and away. It appears that
the section on their ground has collapsed or at least particially
blocked where the ground has dropped. Thus in less than 2 weeks I'm
paddleless!
However as it's 'my' waste but the drain is on their land who's
responsible??

The first thing to do is see what your deeds or Land Registry entry says.
You should also talk to your neighbour.

Peter Crosland