"Needless to say, we are very concerned and, given the time that has passed since Ann was last seen, somewhat fearful as to what may have happened. However there is little we can do other than hope for the best."
The family have now asked for privacy while police make their inquiries.
Bunning, who also goes by Anne Gibbons, had been staying at Te Puru Holiday Park, on Thames Coast Rd, since checking in on January 5.
Earlier this week, the Te Puru Holiday Park's manager told the Herald that Bunning had been living in a small tent near the back of the campsite.
The manager, who did not want to be named, said Bunning was very quiet, had no visitors and was often seen going for long walks. She did not have a car.
The alarm was raised after Bunning was not seen for more than a week and then failed to pay her rent.
The manager discovered her handbag, wallet, credit cards, and reading glasses inside her tent.
"We thought: 'Sh*t, something's wrong here, because she would have her handbag' ... it's gut-wrenching to think about."
Police were contacted and they appealed for anyone who may have seen Bunning to come forward. That plea was repeated this week.
Anyone with information should call Thames police: (07) 867 9600 or CrimeStoppers anonymously 0800 555 111.