James Miller, 34, was shot in the neck by Israeli troops in the Gaza-Egypt border area of Rafah in May 2003 while filming a documentary about the impact of violence in the region on children.
The Israeli army officer who fired the deadly shot - a first lieutenant in the Bedouin Desert Reconnaissance Battalion who was commanding the unit at the time of the killing - was cleared by a court martial last month, despite a military court recommendation that harsh disciplinary action be taken against him.
The Israeli army has since indicated it will reopen proceedings against the officer.
Liz Sich, a spokeswoman for Miller's family, said on Monday in London that lawyers for the family issued a writ on Sunday against the state of Israel. She said she believed that if the case went to trial it would be heard in a civilian court in Israel.
"There is a culture of impunity in the Israeli military"
sister of James Miller
Miller's family says the cameraman and his colleagues, who were leaving the home of a Palestinian family in the southern Gaza city of Rafah after dark, carried a white flag and called out to troops that they were British journalists.
They say that as they walked towards an armoured personnel carrier, an Israeli soldier opened fire and struck Miller with a shot to the neck.
Rafah has been the scene of daily violence throughout more than four years of fighting, and Israeli troops routinely open fire as they patrol the area to protect against ambushes by armed Palestinian men.
In a statement issued Sunday, Miller's widow, Sophy, said the family had indicated in a meeting with the Israeli military in 2003 that they were not prepared to let the case go. She said their resolve had only grown stronger.
"The recent IDF (Israeli Defence Force) decision not to indict the officer responsible and its acquittal of that officer even with the disciplinary measures recommended by the advocate general does nothing to change our perceptions that there is a culture of impunity in the Israeli military," Sophy Miller said.
"It is our hope that as well as accountability for James' death a successful civil case will go somewhere towards changing this and in doing so may make Israeli soldiers think twice about shooting innocent civilians," she said.
Miller (R) was making a feature
on the impact of violence
Miller's sister, Katie, said the family had been given no choice but to issue the civil writ at "enormous personal and financial cost".
"It being the only route left open to finding an approximation of justice for a man who dedicated his personal life to exposing injustice."
The family did not specify how much money they were seeking in damages.