Lady Penelope is very definitive in #2 above:
The neighbouring property is definitely responsible for the damage caused by the roots of their tree.
I don’t understand. Trees have been sending roots out for millions of years. Humans have been using clay pipes with shonky cement joints for a couple of hundred years. Nowadays we know that pores or small cracks in the cement pass moisture, attracting nearby roots which penetrate the cracks, enlarge the cracks, and then grow inside the pipe. So now we use PVC pipes joined with water-repellant adhesive which don’t leak at all. Roots simply don’t know the PVC pipe has water in it and go somewhere else.
So whose fault is the blockage?