A neighbour in England said she smelled a "weird barbecue" in the garden where a badly burned body was found.
The corpse was discovered in the back garden of a house in Southfields, south-west London, on Wednesday afternoon.
A 40-year-old man and 34-year-old woman were arrested at the scene on suspicion of murder and were being questioned on Thursday.
They live with two children, according to neighbours.
A police spokesman said two children had been taken into care following the incident.
He was unable to confirm any lines of investigation linking the victim with those in custody.
One woman, 29, said she was passing the street when she saw what she thought was a "weird barbecue" taking place in a back yard.
She said: "I was going home at about 5.20pm and I smelled this really weird smell. It was like a weird barbecue was going on.
"I could see this light smoke, it was pretty strange."
Officers have been unable to tell the age or gender of the person because the remains were so charred.
Metropolitan Police were called to a property on Wimbledon Park Road just before 6.30pm, after reports that there was a fire and someone had died.
One local man, who asked not to be named, said his daughter came home with a letter from school as a result of the police activity.
A Sheringdale Primary School spokesman told the Press Association: "This is an incredibly distressing incident that has come as a great shock to the whole school community.
"Our priority is of course the welfare of all our children and their families and we will be working now, with the support of the local authority, to provide comfort and reassurance to our pupils, their families and also our staff.
"The Sheringdale community is strong and caring and together we will support each other through this difficult time."
Police think someone had tried to dispose of the body and are appealing for anyone with information to come forward.
Detective Inspector Richard Leonard said: "We are doing everything we can to identify the deceased.
"A post-mortem examination will establish how they died.
"Early indications are that attempts were made to dispose of the body.
"I would like to appeal to those in and around the area to come forward with information.
"You may well have seen or heard something suspicious in the last few days which could assist our investigators."
A body bag was removed from the property at around 4.40pm on Thursday and driven away in a private ambulance, while forensics officers continued their work.