Constance Marten and her boyfriend Mark Gordon broke cover after running out of cash and food, The Telegraph can reveal as the frantic search for their missing baby continued.

Ms Marten, 35, from an aristocratic family, and 48-year-old Mr Gordon had used a slush fund of thousands of pounds to live off grid and evade detection.

But it has emerged that they were forced to take increasingly desperate measures to get provisions after their cash ran out. They are understood to have survived on handouts from food banks for nearly a week before their arrest in Brighton on Monday. 

The pair triggered a police alert that night when they used a bank card to withdraw money from a monitored bank account at a cash machine at a Mulberrys convenience store in the Sussex city. The alert came moments before a member of the public spotted them buying supplies at the same shop and dialled 999. 

The couple’s bank was being monitored by police in case funds were accessed and a location for their whereabouts was then established. 

A Met Police spokesman said: “Simultaneous to the call from the member of the public, the investigation team was alerted to the use of a bank card. The pair were arrested minutes later.”

The couple were seen using a cash machine outside the Mulberrys convenience store on Hollingbury Place on Monday. It was not clear whether the cash withdrawal was the first time Ms Marten and Mr Gordon had used their bank card or activated a police alert that the bank account had been accessed. 

The shop is a short walk from where they were arrested at around 9.30pm after a member of the public who recognised them from media coverage alerted police.

However, staff at both the food bank and shop where the pair bought supplies said nothing was purchased for a baby. 

They had obtained milk, pasta and rice from volunteers at the Brighton Food Bank in the Calvary Church Building last Wednesday, before apparently returning to their makeshift shelter on the edge of the South Downs.

They did not pick up anything obviously intended for a baby such as nappies or powdered milk, which were available at the food bank.

A food bank worker said: “They were given tinned food, bread, pasta, milk and rice. They were not registered with us, which is how we usually operate. The baby was not with them. We have supplies here, but they didn’t ask for anything for a baby. They came asking for help for themselves.”

The food bank worker, who only recognised the couple from photographs after they were arrested, added: “She did the talking. She asked for help. She was wearing a lot of layers and, looking back, she looked like she’d been outside for a while.

“She did the talking. We didn’t take any details, we just gave them food because we thought they needed help.”

They bought “crisps, soft drinks and other provisions” at the shop, a member of staff said. Their purchases did not appear to include anything for a baby.

On Tuesday, police said that while they held out hope that they will find the infant alive, they fear it “may have come to some harm”.

Hundreds of officers are scouring large areas of the Sussex Downs and Brighton. Officers from London Search and Rescue could be seen searching Moulsecoomb Wild Park, around a mile from where the couple were arrested, on Wednesday.

The officers, some wearing jackets indicating they were dog handlers, searched underneath sticks and logs close to where the area meets Hollingbury Golf Course.

A uniformed officer stood guard at the entrance to the park, with dog walkers saying they saw police tape cordoning off parts of the woodland. Searches of nearby allotments continued. 

The couple have refused to reveal the whereabouts of their baby or even tell police whether it is a boy or a girl. They were initially arrested on suspicion of child neglect but were then arrested on Tuesday afternoon on suspicion of gross negligence manslaughter.

The pair had disappeared on Jan 5 after their abandoned car was discovered on fire on the M61 near Bolton, Lancashire. They evaded detection for nearly two months, travelling to Liverpool, Colchester, London and Sussex.

With temperatures on the South Downs plunging to below freezing over the past few nights, many of those who live in the area said they feared the worst.

Danielle Mansell, a 32-year-old mother of three, said: “I just can’t bear to think of that poor baby still being up there, if it’s even still alive, the poor thing. My youngest is just three, and the thought of a little child being out there in this cold – it’s just too unbearable to think about.”

Greenhouses and sheds across the area have been inspected as the police teams search for any sign of the baby, or the blue tent Ms Marten and her partner were reported to have been using to live in over the past few weeks.

Police have searched every shed at the Roedale Valley allotments, near to where Ms Marten and Mr Gordon were arrested, and will remain on site for some time, allotment users have been told.