Fifty-two innocent people were killed in the bombings
UK authorities breached obligations to protect citizens by not acting on details they had about the 7/7 bombers before the attacks, a court has heard.
Lawyers for bereaved families argued that the forthcoming inquests for those killed should examine whether the deaths could have been avoided.
They said MI5 and the police knew a "significant" amount about the four suicide bombers ahead of the attacks.
The 2005 attacks on London claimed the lives of 52 innocent people.
The bombers detonated explosives on three Underground trains and a bus.
Coroner Lady Justice Hallett is holding a three-day legal hearing at the Royal Courts of Justice in central London to decide what form the inquests should take.
Christopher Coltart, representing seven bereaved families, argued that the UK government's obligations to protect its citizens under European law applied to the case.
"In the 15-month period or so leading up to the bombings in July 2005, MI5 and the police were between them in possession of a significant amount of information about the bombers; two of them in particular, Mohammad Sidique Khan and Shehzad Tanweer," he said.
"If, we submit, appropriate, available and proportionate action had been taken at an earlier stage, it may have been possible that the events of 7 July could have been avoided.
"There should now be a full and public investigation of what went on," he added.
The authorities have previously said these issues have been investigated by other inquiries, in particular that of the Parliamentary Intelligence and Security Committee (ISC).
MI5 has argued that the material involved is so sensitive that it would be "contrary to the public interest" for it to be aired in public at the inquests.
But Mr Coltart questioned how effective the ISC inquiry was and said it was impossible to know whether it addressed important questions, because its hearings were held in private.
Meanwhile, the family of a woman killed in the attacks questioned whether the emergency services could have saved her.
Earlier this month, at a pre-inquest hearing, the family of Behnaz Mozakka, 47, heard that she survived for 45 minutes after the blast on a Tube train between King's Cross and Russell Square.
They had previously thought that she had died instantly.
A document submitted to the hearing revealed that 17 of the 52 innocent people killed in the bombings did not die instantly.
Gareth Patterson, representing Mrs Mozakka's family, said they were "entitled" to an inquiry into why she apparently failed to receive "timely treatment".
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.