I don't know anything about the legalities of the situation, but how on earth can it cost £1k+ to fix an obstruction in a known location??? I'm assuming it's not actually under a building?
In the OP's case, the latter applies. I suspect Building Control may be interested in the neighbour's DIY plumbing; alterations to drains are notifiable works.
Not if the blockage is the result of one of the owner's actions.
