Will an insurer cover fixing something like this? It does not seem to
be
storm damage just the general age and wear on the pipe (50 years old).

No, normal ageing is not covered.


Surely damage to other things caused by wear and tear is covered? For
example, if sewage from a worn out drain flows onto the carpets they would
be covered right?


Yes, that would be covered, but the insurers would probably try to claim
their money back from the owner of the drain as their lack of maintenance
caused the spill.