You see, IMO, an open ended cable in the ground will arc and spark and cause no end of problems. It won’t just sit there happily for years. Is the OP really sure no damage was caused? Was he there? Did he say EVERYTHING? This invoice should be passed to his contractor to deal with. He employed them, they rang DNO. There responsibility to settle, argue, or pay with their liability insurance. I really can’t see a cut cable in soil not arcing, burning and ultimately blowing fuses.This seems to be legislation that gives them the right:
http://www.legislation.gov.uk/uksi/2002/2665/contents/made
Its sound very much like the OP is getting a bill for conducting emergency repair work as a result of "Damage" caused by his contractor. I think there is an argument that he discovered a faulty installation that is nothing to do with him or his house and made them aware of it. I would have thought the info is in the letter?