Andrew and Vicki Case, and their two young children Phoebe, aged two and a half and Nereya, aged 18 months, have been found dead at their Fordingbridge home.
Neighbours spoke of their shock following the discovery of the family at Provost Street on Monday, July 26.
Single mum Alayna Brooks, 53, who lives in the same cul-de-sac, said she saw the children's grandmother running out of the red brick terraced house screaming: “My babies are dead; all my babies are dead”.
Miss Brooks said she understood Mr case had been found hanged.
We understand Phoebe and Nereya were on a bed and Vicki (also know by the name Haskell) was found dead in the downstairs dining-room. It is believe the children and mother died from stab wounds.
Mr Case, aged 32, is believed to have been a delivery driver for Doccombe European Ltd, which has a base in Downton Industrial Estate, Wiltshire.
Police tell of horrific scene
The South Central Ambulance crew that attended the scene are said to be so traumatised by what they saw they are to have counselling.
Alayna Brooks, mum-of-three, added: "I'm appalled, upset and I'm shocked. The family had recently come back from a week's holiday in Weymouth.
"I walked back from the shop with the father and the two children yesterday afternoon; the girls are beautiful; they are drop-dead gorgeous.
"They were an amazing family; we all loved them. The couple were so loved up; if I had a marriage I would have loved theirs. It was so upsetting."
Miss Brooks, a loan advisor, went into the house with another neighbour after the grandmother ran out into the street.
She said: "The grandmother picked them up every Monday; she had phoned and when there was no answer she went there. When I went inside with another neighbour there was no sign of a struggle."
Another neighbour Jeremy Pentecost also saw the grandmother running out of the house. He said: "The door was wide open, she was in floods of tears, saying 'I can't believe it.' I think she was on her mobile phone to her husband. The children's dad was a really nice guy. I used to see him cleaning his car and we had a joke together."
Detectives from Hampshire's major crime department are now leading the investigation but say it is too early to say if the deaths are suspicious.
A cordon has been put up around the property.
Acting Superintendent Gary Cooper said it was difficult for his officers at the scene: "It’s very, very difficult clearly. When my officers attended this morning they were met with a quite horrific scene."
Police have said the bodies will be removed from the home this evening. Post mortems on the parents will be carried out in Winchester this evening and on the children on Tuesday.
Eye-witnesses at the scene told how the police cordon had been placed across two houses, to block off the entrance down a small road that leads to more houses. The properties are fairly newly built homes and were being guarded by a policeman.
The road is fairly central in the town and connects with the High Street. The nearest businesses are just a couple of hundred yards away.
Five police cars and two vans were at the scene, with several detectives within the cordon. Officers could be seen getting into white forensic suits as they prepared to go inside the house.
Mayor, Cllr Malcolm Connolly said: “The loss of four young lives is always tragic and it leads to the question why something like this happens. I’ve only just taken it in.
“It’s a small town and these people will have been known to many and this will have a major impact.”
He was unable to say who the victims are, but said: “It’s such a waste of life.”
Retired butcher David Price, whose business is on Provost Street, said: “It’s a tragedy, I don’t know what's behind it.”
And at Caxton Décor, employee Mike Jones said: “It’s a bit of a shock to say the least, because it might be somebody who comes into the shop.” He too was unaware of the victims' identity.
A member of staff from the Kebab House said: “When I arrived there were police everywhere, initially three or four cars but maybe more. People are just walking up and down trying to find out what has happened.”
Staff at the nearby Crown Inn said regulars in the pub were talking about what was happening but nobody really knew for sure what had taken place.