Jamie-Leigh Kelly, 31, left the centre on Tuesday with her three-year-old daughter and newborn baby boy.
A Metropolitan Police statement said the children were found at an address in Harwich on Sunday, but officers are still trying to locate Ms Kelly.
Jamie-Leigh, I continue my direct appeal to you to contact us
Detective Superintendent Lewis Basford
The children were taken into police protection and then to hospital as a precaution.
Detective Superintendent Lewis Basford, who is overseeing the investigation, said: “We are very pleased, and of course relieved, to have found the two children after extensive enquiries over the past few days.
“They are safe and well and receiving precautionary medical attention.
“Jamie-Leigh was not present and our work to locate her continues.
“I urge anyone who may have helped facilitate the movement of the children, or who may be assisting Jamie-Leigh with transport or accommodation, to come forward to police now.
“Jamie-Leigh, I continue my direct appeal to you to contact us.
“We are asking you to please pick up the phone and have a conversation with us so we can meet with you.
“Please contact us on 020 7175 0793 or go to a police station as quickly as possible.”
A 63-year-old woman was arrested at the address in Essex on Sunday on suspicion of child abduction, assisting an offender and perverting the course of justice, a Met spokesperson said.
She remains in custody at an east London police station.
Ashley Hawkins, 52, of Alex Guy Gardens, Dagenham, and Jordan Hardy, 30, of Connor Road, Dagenham, are due to appear at Southend Magistrates’ Court in Essex on Monday, charged with two counts of child abduction, the force said.
