Constance Marten and Mark Gordon are held on suspicion of gross negligence manslaughter.
on Tuesday, Det Supt Lewis Basford urged the public to help with the search and report any potential sightings in Brighton and Newhaven.
"Equally if you are out walking in these areas and you discover something you think we should know about, please don't hesitate to contact us, no matter how insignificant it may seem." After their car was found on fire, police said the family left the scene and travelled to Liverpool, Essex, London and East Sussex.
Their home is in Eltham, in south-east London, but they have been living nomadically since September last year - when Ms Marten first started to show signs of pregnancy.Police have not ruled out that someone could be looking after the baby - though they added this was unlikely.
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