Police searching for a missing couple and their newborn baby believe the family has been sleeping in a tent in sub-zero temperatures.
Officers have been trying to find Constance Marten, 35, and Mark Gordon, 48, since their car broke down on the M61 near Bolton on 5 January.
Police say they went into an Argos in Whitechapel, in east London, two days later to buy camping gear.
They say Gordon, a convicted sex offender who served 20 years in a US jail for rape and battery, went alone and bought two big bags of items, including a blue two-man tent, sleeping bags and two pillows.
The family was last seen walking along Brick Lane, towards Bethnal Green Road at about 10pm.
Detective Superintendent Lewis Basford, who is leading the investigation, expressed his concern for the safety of the newborn baby, who he believes has been exposed to sub-freezing cold temperatures, and urged the public to look out for the family.
He told Sky News: "I don't believe the couple would intentionally look to harm the child, but just by the very nature of the environment that we believe that they are now in, there is a significant risk to the baby, who was only a couple of days old on 7 January."
He said the couple are "well travelled" adding: "We've seen with the sort of the chaotic movements in the first few days of the investigation, that they are happy to travel. We know they have taxis. I'm really, really pushing it out to the wider public - certainly taxi drivers - as we know that is their preferred method of transport."
Earlier, he said: "No child, especially a tiny, newborn baby, should be forced to endure such dangerous, potentially life-threatening, conditions.
"This is why it is absolutely vital that anyone with information about their whereabouts contacts us as a matter of urgency - whether it is with a recent or older sighting. Every piece of information is crucial to enabling us to find the baby and ensure it is okay.
"My officers will continue working tirelessly behind the scenes to piece together the family's movements and current whereabouts. It could be that they are trying to blend in with homeless communities, either here in London or further afield, or they could be camping in more rural or wooded areas.
"They could be absolutely anywhere in the country. Please keep your eyes peeled, especially while you are out and about in waste ground or beauty spots, or while you're walking the dog, and report any information, no matter how insignificant you think it is, to us."
On 5 January, police were called to the hard shoulder of the M61 where a car Ms Marten and Mr Gordon had been using was on fire.
It is believed most of their belongings were destroyed in the blaze.
Police say Ms Marten, who grew up in Crichel House, a Dorset estate, as part of an affluent family with links to the royals, may have given birth just a day or two before the fire but neither she nor the baby were assessed by medical professionals.
Sightings of the couple were then reported in Liverpool and Harwich before they were seen in Colchester, Essex, on 6 and 7 January.
Detectives have now established that they took a taxi from East Ham in east London, being dropped off in Whitechapel Road at 6.14pm on 7 January which is where they appeared on CCTV.
There have been no reported sightings of the couple since then.