reports that the distraught husband told police about the moment he was attacked by the three men.
He said: "It was shortly after five. I saw three hooded men. One was tall. They shouted and threatened in broken Greek.
"They tied me to a chair and then went on my wife."
The same report quotes the pilot as telling police he was sleeping downstairs during the break-in
“When I managed to break free, I rushed upstairs to the attic to find my wife on the floor facing down, and the baby next to her wailing,” he reportedly told cops.
Charalambos called the police around 6am.
The Greek government has issued a £258,000 reward for information leading to the arrest of the men, reports The Dawn.
Police said it appears that the robbers were experienced and likely watched the couple for some time before the raid.
The gangsters reportedly broke into the home through a window in the basement before killing the family dog in the first floor of the property.
When they fled the home, they left the dead hound hanging a fence outside the house.
Officers are trawling through CCTV to see how the gang got away and whether they were in the area before the raid.
Police spokesman Theodoros Chronopoulos described the murder as a "heinous crime, committed with extreme ferocity."
He added: "We’ve seen several other ugly murders throughout the years. But this was extremely brutal and violent.”
The murdered woman was born in Greece but had a British passport, the police said.
Mrs Crouch was a student at the University of Piraeus and on her husband’s Instagram account the couple are pictured smiling with their baby.
Greeks are used to gangland killings but the strangling of the woman in front of her child has led to shock in the country.
Haunting social media videos of Brit mum, 20, who was tortured to death in front of her baby daughter while pilot husband, 32, tied up by burglars in Greece