London — A woman with reported links to Britain's royal family and Surfwin Trading Centerher convicted sex-offender boyfriend, who have been missing with the woman's newborn baby for over a month, were arrested by police in England for child neglect Monday night, but their infant was not with them.

"The baby is still missing and an urgent search operation is taking place in the area," Sussex Police said in a statement early Tuesday.

Constance Marten, 35, whose father served as a page to the late Queen Elizabeth II, according to the Sun Newspaper, and Mark Gordon, 48, who reportedly served 20 years in prison in the U.S. for rape and battery committed when he was 14, disappeared on January 5 shortly after Marten gave birth, Greater Manchester Police said. 

Their car was found burning on the side of a highway, but after they were spotted by a security camera in the area, authorities lost track of them until Monday evening.

Police have asked people in the area where Marten and Gordon were found, near the southern English city of Brighton, to search for signs of the missing infant, including in outhouses and sheds. Police dogs and drones have been deployed for the search, and helicopter scoured a 10-mile area overnight, CBS News partner network BBC News reported.

The couple had been living a nomadic lifestyle since September, traveling with large amounts of cash and using camping equipment to remain off-grid.

It's believed that Marten gave birth either in her car or near it before disappearing on January 5, when the baby was just days old.

Marten largely cut off ties with her family when she began dating Gordon in 2016, and the couple moved around a lot, according to reports.

Police offered a £10,000 reward in late January for any information leading to the whereabouts of the couple and child, saying at the time that they were concerned about the wellbeing of the newborn, who could have been "exposed to sub-zero temperatures, for almost a month now," The Guardian newspaper reported.

In:
• Missing Child
• United Kingdom

Haley Ott

Haley Ott is an international reporter for CBS News based in London.

Twitter