He was expected to return to the capital, Port Moresby, last week but has not been seen. Allen was not carrying a mobile phone or GPS device.
The BBC say the helicopter pilot who dropped Allen off weeks prior is now searching for him.
Allen's sister, Katie Pestille, told BBC Radio 4's Today programme (via The Independent): "He knows all about that survival stuff. It's just what worries me is there are bad people in these jungles.
"You would think that they were totally empty but there are people in there. I mean, I know more about the Amazon, but there are loggers and drug dealers and all sorts of bad people."
Fellow adventurer Ben Fogle and BBC security correspondent Frank Gardner shared their concerns online...
Allen has previously crossed the Amazon Basin on foot, found his way through a six-week male initiation ceremony where crocodile marks were carved onto his body, and crossed the central mountain range of New Guinea.
On Allen’s website, the last entry on his blog is titled: “I may be some time …”
In it, he writes: “The Yaifo, a band of people I made first outside contact with some 30 years ago, are still living in the remote Central Range of PNG. Furthermore, no outsider has made the journey to visit them since the rather perilous journey I made as a young man three decades ago. This would make them the remotest people in Papua New Guinea, and one of the last people on the entire planet who are out-of-contact with our interconnected world.
“In October I’m hiring a helicopter to drop me off at the abandoned mission station, Bisorio … If – and only if – it seems ethical, I’ll try to assemble a small party, as I did all those years ago, and head off up-slope into the mists to visit the Yaifo in their remote abode. The aim is to create a brief record of their lives…”
