Justice Heather Hallett, who is overseeing the inquests into the deaths of the 52 people killed in the suicide attacks, ruled earlier this month that she could not hear evidence detailing sensitive intelligence material in closed session.

She concluded that even if the public could be excluded, "interested parties," such as relatives of the victims, could not.

May mounted a legal challenge to that decision, arguing that disclosing secret information could put Britain's national security at risk.

However, the High Court upheld the coroner's decision.

"It is right that those who lost their loved ones should be able to see and hear all the evidence," said lawyer Clifford Tibber whose firm is representing relatives of six victims.

"It is difficult to understand what information, six years on, is so sensitive and so critical that it can not be made available to the families in some form."

A Home Office spokeswoman said the government was committed to co-operating fully with the coroner.

"Along with many victims' families, we believe a closed hearing for a small part of the July 7 inquests would be the best way for the coroner to consider as much information as possible," the spokeswoman said.

"The court has decided this is not possible and we will consider the judgement carefully."