Mr Jones said the house was insured, but not with AMI. Its capital value was $1.05 million, according to Auckland Council records.
The property had been in the family for more than 80 years and was a destination for many holidays when Mr Jones was a child.
He and his wife, Sue, lived on the same street and rented the bach over summer. The last tenants moved out on Wednesday afternoon.
Mr and Mrs Jones were woken by fire engines and watched their house burning down. No one was inside.
A northern fire communications spokesman said the building was gutted within 30 minutes.
Fire investigator Linda McHugh said the blaze appeared to have started in the lounge and investigators were sifting through debris searching for an ignition source.
An AMI spokesman said the bach was chosen because it had charm and character and was not ostentatious.
"Kiwi baches pull at the heartstrings so you could say that a little bit of what's great about New Zealand has been lost."