The 47-year-old and the boys, nine and seven, were discovered on Mayfield Road in Belvedere, south east London, at 11.50am yesterday.
The house was sealed off with police tape today following the discovery.
One police van and a forensics services vehicle could be seen outside the 1940s three-bedroomed terraced house.
The driveway, which has a grey Mitsubishi pick-up truck parked on it, is scattered with children’s toys, including a mini basketball net and multi-coloured sand toys.
Two officers were seen leaving the property, which has a “beware of the dog sign” on the front door, with two boxes of evidence.
Shocked neighbours have spoken of their horror following the tragic incident.
Marion Beazer, 69, who lives opposite the family, said as far as she could tell they were a “normal family”.
The pensioner, who has lived in the street 40 years, added: “They never caused any issues in the street.
“As far as I’m aware they were just a normal family. They kept themselves to themselves.
“The neighbours here really watch out for each other.
“Seeing the kids toys out the front tugs on the heart strings. It’s just dreadful.”
Marion said she had two police officers in her house going through her CCTV to check for anything unusual.
Another neighbour, Christopher Babutulde, 68, who lives two doors down from the family, said he used to see the mum walking her sons to and from school.
He added: “It’s really shocking. We’re such a close knit community who really care for each other.
“There’s been a big police presence since yesterday. I’ve had officers knocking on my door.”
A third, Booja Kaur, 42, said: “I’m so shocked. I saw the lady sometimes taking her kids to school. ”
A fourth neighbour, who asked not to be named, said he believes she previously had a partner living at the property but that neighbours had not seen him around for a while.
He said: “My friend over the road said she hadn’t seen the husband for quite a while.
“I used to see the grandmother wheeling the two kids around in a wheelchair.
“And I used to see the family walking up to the park and the post office and would say hi. But they kept to themselves really.
“Its awful. It’s just too close to home.”
A spokesperson for Metropolitan Police said: “Detectives are investigating following the deaths of three people at an address in south London.
“Police were called at 11:50hrs on Thursday, 9 March to concerns for the welfare of occupants at an address on Mayfield Road in Belvedere.
“Officers and London Ambulance Service attended. At the scene, a 47-year-old woman and two boys, aged nine and seven, were found deceased inside the property.
“Next of kin have been notified.
“Post-mortem examinations will be arranged in due course.
“The Met’s Specialist Crime Command is leading the investigation.
“At this early stage, detectives are not actively seeking anyone else in connection with the investigation.
“A crime scene remains in place.”
A London Ambulance Service spokesperson said: “We were called at 12.16pm yesterday (9 March) to reports of an incident on Mayfield Road, Belvedere.
“We sent a medic in a fast response car and two incident response officers to the scene.
“Sadly three people were pronounced dead at the scene.”