Zandile Tshuma, 42, and her daughters Natalie, 15, and Nala, five, were found dead at their £1.2million home in Great Denham, Bedfordshire.
Officers made the grim discovery after forcing their way into the family home amid concerns the trio had not been seen for several days.
Cops launched a murder probe and later identified Ndodana Tshuma, Zandile’s husband and father to the two girls, as the prime suspect.
CCTV released by Bedfordshire Police showed Tshuma at Heathrow Airport, with fears growing that the 45-year-old has fled to Zimbabwe.
And heartbroken neighbours have since revealed that the pair’s marriage was on the rocks, with Zandile reportedly demanding a divorce.
One resident, who asked not to be named, told The Sun: “What has happened is utterly heartbreaking.
“I didn’t know the family very well but they seemed to have it all – two beautiful girls, great jobs and a lovely big house with a swimming pool.
“But then we heard on the grapevine that the house had recently being valued and they were putting it on the market.
“Someone said they were splitting up with divorce on the cards and it was very bitter because the girls were going to be living with their mum.
“The dad is a powerful and influential businessman and, I understand, rather controlling.
“We don’t know the ins and outs of why they were separating, it’s none of our business.
“But it was surprising because they had seemed to be the perfect family when they moved in but had become a broken one.”
Suspect Tshuma – a British citizen of Zimbabwean heritage – is believed to have flown to Zimbabwe on a British passport on July 4.
Officers have now issued a direct plea to the dad, who is wanted in connection with all three deaths.
A former neighbour of the family said news of the alleged triple murder was “shocking and sickening”.
She told The Sun: “They seemed like a really nice couple who were always busy working and kept themselves to themselves.
“No one really got to know them here. I don’t know what jobs they did but they came across as successful and well off.
“They were so looking forward moving into their dream home. I can’t believe what has happened. It’s so shocking and sickening.
“My heart goes out to that poor wife and her kids. I hope police catch the suspect as quickly as possible.”
The detached four-bedroom, four-bathroom property, complete with a swimming pool, was bought around two years ago for £1.3million.
Another woman, who laid flowers outside the family home, said: “We are really sorry to lose her, she was such a gracious mother.”
Major crime units from Bedfordshire, Cambridgeshire and Hertfordshire Constabulary are leading the investigation.
Detective Inspector Lee Martin, senior investigating officer, warned that “criminal investigation knows no borders”.
Issuing a statement, he said: “We know that Mark Tshuma left the country on Saturday and is now believed to be in Zimbabwe.
“We are urgently working to find and apprehend him, and would appeal to him directly to hand himself in.
“Mark, unthinkable harm has been caused to those around you, and this has left your relatives and friends utterly devastated.
“We are actively working with national and international agencies to pursue every available line of enquiry to track you down.
“Please do the right thing, come forward and hand yourself in to local authorities.
“Our thoughts are still very much with Zandile, Natalie and Nala, as well as all of those who loved and knew them, at this extremely difficult time.”
