The couple, who are believed to have moved to the area four years ago, have been taken to separate south London police stations where they are being questioned.
Meanwhile, forensic officers were seen yesterday removing a body from the garden of the property after emergency services were called following reports of a fire.
Last night, Scotland Yard announced that a murder investigation had been launched and was being led by Homicide and Major Crime Command. However, due to the extent of the burns to the victim's body, they are yet to identify them.
Speaking to The Daily Telegraph, Sunny Patel, who runs the newsagents opposite the couple's home, said that he had seen smoke rising from their garden yesterday, but had thought nothing of it.
He said that the couple had a French-speaking au pair who looked after their two children, adding that she had not been seen for several weeks.
"I have not seen the nanny since late August. She used to come in with the kids twice a day to buy them sweets," he said.
"She looked about 13 but was actually in her early 20s. A very polite pleasant girl. She was French. The family was also French. The nanny has lived her for at least 20 months, she was here last Christmas.
"They are a French family, but the husband works abroad in France I believe. Last night I saw plumes of smoke coming from the garden - lots of smoke, not much flames - but just thought it was a garden fire.
"Then last night we were told that the man was arrested and then his wife."
Another woman who had been passing by the property on Wednesday evening said a "weird smell" was coming from the fire, adding that she thought the family were holding a "weird barbecue".
A neighbour living above the couple's apartment said they had been forced to ring their landlord on Tuesday because there was a "bad smell".
"On Tuesday we rang the landlord because there was a bad smell, we thought maybe a gas leak," they said. "The landlord looked around our flat but couldn't find anything."
One neighbour, who asked to remain anonymous, said that he had seen the au pair "intermittently coming and going" from the property in recent months but had not seen her for "some time", adding that she was a "shy and rather slim looking girl".
Another said that her children had watched from their bedroom window on Wednesday evening as a man started a fire and began burning items in the couple's garden.
"They [my children] were in the bedroom and told me he had started a big fire and was brushing wood into it. The man saw them and started making grunting sounds at them like he was drunk.
"I often spoke to the nanny to say hello and to throw the children's ball back. They were always up late and a bit wild."
The couple's two children, who attend a local primary school, were taken away by social services yesterday following the couple's arrest, a police spokesman said.
"We saw them put the boys in the back of a car once the police arrived," one neighbour said. "Officials were with them."
In a statement, the school said: "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 Met's detective inspector, Richard Leonard, said: "A badly burned body has been found in the rear garden of this residential address. 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."
