A member of the public reported seeing Constance Marten and Mark Gordon in Stanmer Villas, Brighton, shortly before 9.30 p.m. on Monday, February 27.
Sussex Police officers responded to the scene and arrested the pair. They are still being held.
The Metropolitan Police have launched an urgent search to find their baby, who has not received medical attention since his birth in early January.
Marten, 35, and Gordon, 48, have been taking taxis around the UK since their car caught fire on the M61 in Bolton, Greater Manchester, on January 5.
According to police, Constance Marten (pictured) and Mark Gordon were seen in Stanmer Villas, Brighton, shortly before 9.30 p.m. on Monday, February 27.
Previously, authorities believed the couple had been sleeping rough in a blue tent and had avoided being tracked down by police by moving around frequently and hiding their faces in CCTV images.
The couple travelled from Bolton to Liverpool, then to Harwich in Essex, east London, and finally to Newhaven in Sussex, where they were spotted near the ferry terminal on January 8.
Miss Marten, who comes from a wealthy aristocratic family, was a promising drama student when she met Mr Gordon for the first time in 2016.
Since then, the couple has lived in seclusion, and in September, when Miss Marten was well into her pregnancy, she began moving around rental apartments.
It is unknown if their baby was born full-term or if he or she has any health issues.
Anyone who can help in the search for the couple’s baby is asked to call 999.
This is a developing story that is being updated.