Detectives have told a cousin of Jean Charles de Menezes his number was found on the phone hacking list of a News of the World private investigator.
Other people connected to the young Brazilian shot dead by police marksmen at Stockwell Tube station in 2005 fear they too may have been targeted.
Relatives, campaigners and members of the family's legal team have given police their phone numbers so officers can check whether they were victims of hacking.
Mr de Menezes, 27, was shot dead by counter-terrorist officers hunting would-be suicide bomber Hussain Osman the day after the failed July 21, 2005 attacks on London.
His family said that officers from Operation Weeting, Scotland Yard's new phone hacking inquiry, confirmed yesterday that the mobile phone of his cousin Alex Pereira was found on a list compiled by private investigator Glenn Mulcaire.
A spokesman for the Justice4Jean campaign said: "The Menezes family are deeply pained to find their phones may have been hacked at a time at which they were at their most vulnerable and bereaved.
"They are bewildered as to why the police did not approach them with this information earlier, and fear the police may be attempting to cover up their own wrongdoing once more relating to this case."
Mr de Menezes's family today called on David Cameron to widen the scope of the phone hacking inquiry to look at alleged police leaks to the media during the investigation into the Brazilian's death.
They highlighted in particular the role of former Scotland Yard assistant commissioner Andy Hayman, who is now a columnist for The Times, a sister paper of the News of the World in Rupert Murdoch's News International group.
Relatives of Mr de Menezes wrote to the Prime Minister: "We are conscious that the newspapers owned by News International provided some of the most virulent and often misleading coverage around Jean's death and its aftermath.
"Throughout the investigation, misinformation continued to be leaked to the press that attempted to besmirch Jean's character.
"The publication of these lies about his actions on the day of the shooting included false allegations that Jean Charles was wearing a bulky jacket, had failed to stop after a police warning, had jumped the ticket barriers or had acted suspiciously in the moments leading up to his shooting.
"They also related to untrue allegations about his immigration status and even attempts to link him to a rape allegation that could only have emanated from police sources."
The family went on: "Considering what is now known about Andy Hayman's relationship with News International, we would like the inquiry into this scandal to extend its remit to scrutinise whether police officers involved in the Menezes investigation were leaking information to the press, either for financial benefit or in a vain effort to deflect criticism from the actions of the Metropolitan Police which had led to Jean's death."
Mr Hayman strongly rejected suggestions that he was in News International's "back pocket" when he gave evidence to the Home Affairs Select Committee this week.Reuse content