The Wolfs made aliyah 30 years ago and were at home when the rocket struck with their son, daughter-in-law, daughter and two small grandchildren, aged two and five months.
One member of the family, Daniel Woolf, described the moment of impact to the JC: “There was a boom, then quiet and dust everywhere, and then screaming. It was terrible.”
Speaking to the press outside the house, Robert Wolf said: "With all the games of politicians and all them blowing out their chests and they're all wonderful people and they're all great people and they're all going to save us, this is the real price. And I just paid it.
"And I nearly lost my family. And if we hadn't got to the bomb shelter in time I would be burying all my family. That's two nechadim, two grandchildren — one five months, one two years old.
"That's my third child with his wife, my wife, myself and my daughter, my youngest daughter. They would all have been dead if we didn't do... sorry... if we didn't do what we were supposed to do.”
David Quarrey, Britain's ambassador to Israel, tweeted: "Our thoughts are with the British-Israeli family whose house was hit."
The news prompted Benjamin Netanyahu to cut short his trip to the US and return after meeting with President Donald Trump.
He will not deliver his speech at the 2019 Aipac conference on Tuesday as originally planned.
Mr Netanyahu said he would return to Israel "to manage our operations up close," having held a briefing with the military chief of staff, head of the Shin Bet security service, and head of the National Security Council.
While no one in Gaza has claimed responsibility for the rocket fire, sources in Hamas said the group's leader in Gaza had cancelled a planned speech.
They also said senior figures in the organisation had gone into hiding due to fears over an Israeli response.
It is understood that Iron Dome defence system had not been activated when the rocket was launched from Gaza.
It is believed that the rocket was fired from the southern Gaza Strip, which is some 62 miles away from where it struck.
According to Israeli intelligence sources, Hamas and Islamic Jihad are the only groups in Gaza who have access to rockets with that range.
