On his website, Mr Allen wrote: 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. "Marching off to Heathrow".
He had no telephone or Global Positioning System device with him for the trip which was expected to take him through very remote areas of jungle.
He had been trying to reach the Yaifo, a reclusive tribe that he had met on a similar trip about three decades ago.
His sister, Katie Pestille, told The Daily Telegraph she wished she had badgered him to take communications equipment on the trip. "Maybe he miscalculated the distance he's going to have to cross on the way back, or there could be obstacles", she added.
She added: "We don't think that he has [a mobile phone] and I wish I had insisted that he take one with him, because for a situation like this it would be invaluable". She added: "They are seriously anxious".
"Landslides, torrential downpours and sometimes an eruption of fighting between local tribes can all throw itineraries off-course" in Papua New Guinea, says the BBC's Frank Gardner. "But of course now they know he's in danger, they are seriously anxious".
"I am trying to stay positive and hope it's going to end up well and he will come out of the jungle soon".
While the family isn't necessarily anxious that the Yaifo have done something nefarious with Allen, given his past relationship with them, there are other dangers in the wild, such as loggers and drug runners, that may be at play.
She recalled: "When he was younger he went from the mouth of the Amazon to the mouth of the Orinoco, through all this uncharted terrain. It's an very bad worry, if they came across him they could have robbed him and just left him there".
But despite Mr Allen being a grizzled explorer who once ate his own dog to survive, fears have been raised for his safety after he failed to start his journey home.
A search has been launched, led by the helicopter pilot who dropped him off.
"I'm hiring a helicopter to drop me off at the abandoned mission station, Bisorio - a forlorn place".
In a September blog post titled "I may be sometime", he wrote: "The Yaifo are one of the last people on the entire planet who are out of contact with our interconnected world".
Last time (see The Proving Grounds), the Yaifo "greeted" me with a terrifying show of strength, an energetic dance featuring their bows and arrows. "On this occasion who knows if the Yaifo will do the same, or run off, or be wearing jeans and T-shirts". So, if this website or my Twitter account falls more than usually silent - I'm due back mid.
A Foreign Office spokesperson said: "Our staff are assisting the family of a British man who has been reported missing in Papua New Guinea, and are contacting the local authorities".
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