"The Kelly family are not seeking revenge or retribution against individual scapegoats" but feel that "the duplicity of the government should be exposed", said lawyer Jeremy Gompertz on Thursday.
"Never again should there be such feeble support for an employee at a time of crisis," he added.
Kelly, 59, was found dead with a slashed wrist in woodland near his countryside home on 18 July, days after being "outed" by the Ministry of Defence as the suspected source of a BBC report that the government "sexed up" a controversial dossier on Iraq and weapons of mass destruction.
Over the last two months, Prime Minister Tony Blair's administration has been put under a harsh spotlight by Lord Hutton’s judicial inquiry into Kelly's death.
After taking 110 hours of evidence and lifting the lid on the world of British intelligence, Hutton heard closing statements from counsel on Thursday.
His final report is not expected before November. Hutton has said no one will be immune from criticism.
Davies defends BBC
BBC chairman Gavyn Davies had defended the independence of Britain's public broadcaster and the credibility of its journalists on Wednesday.
Under cross-examination on the final day of testimony, Davies said that BBC governors had acted correctly in supporting Andrew Gilligan, the journalist who reported in May that Prime Minister Tony Blair's office had embellished an intelligence dossier on Iraq and weapons of mass destruction ahead of war.
Lord Hutton says no one will be immune from criticism
"I think it was perfectly reasonable for me to take the view that the public would look to the governors to stand up for the independence of the BBC," Davies said.
Davies robustly denied a charge from government lawyer Jonathan Sumption that BBC governors at a key meeting on 6 July had been too quick to back the public broadcaster's management and Gilligan.
The governors were "highly experienced and independent minded people" who did not do it for monetary reward, and had nothing to gain "by supporting management for the sake of it", Davies said.
Kelly's widow told the inquiry that faced with the prospect of being identified as the source of the BBC's report, the former United Nations arms inspector was under huge stress and felt betrayed by his employers.
The government's dossier had claimed that Iraq could deploy chemical or biological weapons in just 45 minutes, though it failed to specify that it was referring to battlefield weapons rather than long-range strategic weapons.
Blair support slumps
Kelly's death and increasing concern over Blair's decision to contribute over 40,000 British troops to the US-led invasion of Iraq in March, have left the prime minister facing the worst crisis of his six years in office.
Blair’s popularity has slumped over the summer so that now 61% of voters are unhappy with the job he is doing, an opinion poll showed on Thursday.
Tony Blair has lost the trust of most British voters
His rating for trustworthiness has fallen nine points since July to just 30%. An overwhelming 70% say he is far too concerned with public relations and "spin doctoring".
Blair's troubles over Iraq mounted after a senior US official said on Wednesday that an initial report from inspectors searching for weapons in Iraq was expected to say they had found no proof of actual arms but merely "documentary evidence" that Iraq had biological weapons programmes.
Under fire over the failure to find banned weapons in Iraq, Blair has told his critics to wait for the report by the Iraq Survey Group, led by weapons inspector David Kay.
British Foreign Secretary Jack Straw told BBC radio he had only seen extracts from the report, but he stressed that it was a "work in progress" by the survey group.
"Its work will continue in what everyone understands has been a pretty hostile and difficult environment," he said, speaking from New York.
Asked if he was still confident that evidence of weapons programmes would be found in Iraq, Straw said, "I hope so."