The suspicions that the hijackers of the Afghan plane - and possibly some passengers - want to stay in the UK follow comments by Ariana airline head Mullah Hamidullah.
He told the Afghan Islamic Press news agency, quoting a steward released during the plane's stopover in Tashkent, that there appeared to be a large group on the aircraft of up to 40 men, women and children who could be involved in an attempt to get political asylum.
The Boeing 727 is spending its third day at the London airport after being hijacked during an internal Afghan flight on Sunday. Some 156 people are still on board in deteriorating conditions.
Click here to watch live coverage of the hijack.
An official from the United Nations High Commission for Refugees has also arrived at the airport, although spokesman Paul Wilkinson refused to speculate that political asylum was the reason for the hijack.
But he added: "Conditions in Afghanistan are very very bad, very very miserable and people are often driven to extremes in these circumstances - especially when it has been going on so long and no end is in sight."
Eman Omar, a solicitor who represented a gang responsible for Britain's last hijack crisis, in 1996, said she believed the Stansted group were "highly likely" to be seeking asylum in the UK.
Essex police assistant chief constable John Broughton said: "No specific demands beyond house-keeping requirements have been made, incredible as that may seem."
If the hijackers do try to claim political asylum in the UK, they may be encouraged by the fates of others involved in similar incidents.
Six members of a gang that forced a hijacked Sudanese jet to Britain in 1996 are still living in the UK on benefits while they await an adjudication on their claims, while a man involved in a 1982 Air Tanzania hijack was granted asylum here after serving two years of a three-year jail sentence.
Under international law the UK is obliged to consider any asylum claim submitted once any potential criminal proceedings are completed.
The overnight escape, in which the crew members jumped from a cockpit window and ran to safety at 2300 GMT, caused tension but the situation has returned to normal, police said.
They are questioning the four, hoping to gain fresh information on conditions inside. Police have already established that the hijackers are carrying handguns.
The familiar routine of recent days has now been re-established, with hot food and medical supplies being delivered to the plane, in a quiet corner of Stansted Airport.
Four hours later a flight attendant was pushed down the steps. He was treated for a minor cut on his forehead.
Police said they were unable to speak to the hijackers at all for about an hour afterwards.
In Afghanistan, the ruling Taleban movement has arrested 10 people in charge of security at Kabul airport over the hijacking.
Also:
Pilots criticised for fleeing
Hostages 'face horrific ordeal'
Who are the hijackers?
Negotiating with hijackers
Stansted's hijack history
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