Rose Addis's case has generated a political storm
The accusations were made by the Conservatives, who said the breach happened during briefings to journalists over the care given to Rose Addis.
Speaking on BBC Radio 2's Jimmy Young Show, Mr Blair denied accusations that Number 10 had acted incorrectly.
Family claims: Mrs Addis was left caked in blood
Hospital claims: Staff tried to change or bathe her
Family claims: Mrs Addis was treated worse than a dog
Hospital claims: She received prompt treatment
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He added that the Tories had raised the case, and he had been "perfectly justified" to put the other side of the story.
He also denied that he was being hypocritical by discussing other people's medical details in public while refusing to reveal whether his son Leo had received the controversial MMR vaccination.
He suggested that by going to a newspaper with their complaints, Mrs Addis's family had effectively made public debate about her case acceptable.
The row erupted when Tory leader Iain Duncan Smith criticised the way a north London hospital had treated Mrs Addis.
No regrets
At a stormy Prime Minister's Question Time on Wednesday, Mr Duncan Smith quoted the pensioner's family saying she had been treated worse than a dog, prompting Whittington Hospital to demand an apology from the Conservatives.
Mrs Addis was admitted to the Accident and Emergency unit on Sunday after injuring her head in a fall at home.
Her relatives say she was left unwashed and caked in blood for three days in casualty - but the hospital insists that she received appropriate treatment.
Racism allegation
Mr Duncan Smith also reacted angrily to suggestions from the hospital that Mrs Addis had refused to be treated by ethnic minority nurses - a claim rejected by her family.
Mrs Addis grandson was also angered by the racism suggestion.
"To imply we could be racist just illustrates the bankruptcy of the hospital's case," he told BBC News.
'Political football'
John Edmonds, general secretary of the GMB union, said his members who worked at the Whittington and throughout the NHS were "sick and tired of being used as a political football by both parties."
"There are problems facing the NHS, but one of them is not the quality and dedication of its staff.
"It is time for the politicians to stop running down public service workers and to start working with them," Mr Edmonds said.