Police believe the 45 year-old mother-of-two was attacked on her journey, after a post-mortem examination determined that she had been strangled and hit over the head.
She had been walking back from King Georges Hospital in Ilford and had been making her way to Barley Lane in the direction of the A12.
The suspect remains at an east London police station and Ms Rawlings’s family have been informed about his arrest.
Detective Chief Inspector David Hillier, the head of the murder investigation, said: “My thoughts remain with Maria’s family at this incredibly difficult time.
“I continue to appeal for anyone with information to contact police.”
Given safety concerns after the murder, the police have increased their presence in the area where the crime took place.
Chief Superintendent Stephen Clayman, the Metropolitan Police’s Basic Command Unit Commander for Barking and Dagenham, Havering and Redbridge, said: “I understand the concerns around safety that will arise from this, particularly from women, and we have increased patrols in the area from our local policing teams.”
Those with information can contact the incident room on 020 8345 3865 or by calling 101 or tweeting MetCC, and quoting the reference CAD3551/4May.