But each advance they make in their investigation uncovers new and disturbing questions.
Working from surveillance video, investigators noted four men who met at King's Cross rail station on 7 July, shortly before the bomb blasts ripped through three metro trains and a double decker bus.
Personal documents thought to belong to three of these suspects have been found near the scenes of the explosions, allowing identification.
Peter Clarke, an antiterrorist official with the London Metropolitan Police, on 12 July was able to announce the first arrest in the case.
"One man has been arrested in West Yorkshire [in northern England], and will be brought to London to be questioned," Clarke said.
The arrested man is thought to be a relative of one of the main suspects. The present whereabouts of all the main suspects is unknown: police are considering the possibility that one or all of them were killed in the bomb blasts.
But the most ominous news is that authorities believe most of the suspects were of Pakistani origin but born in Britain and raised in the provincial city of Leeds in Yorkshire. One of the bombers is thought to be from Luton, an industrial town just north of London. Both cities have large Muslim populations.
If these facts are correct, the implications are grave indeed.
It would mean that instead of having to deal with a handful of foreign terrorists who arrived in England on a single terrorist mission, the British authorities are facing a domestic terror scene that has been able to secretly nurture, train, and equip British citizens for a major attack on one of the world's great cities -- all under the noses of the police and intelligence communities.
London-based security analyst Chris Langton of the International Institute for Strategic Studies says the events are a setback for national security.
"This is a blow to the security of the country in that this happened without anybody being aware that it was imminent -- particularly because the extensive surveillance and intelligence-gathering activities that have gone on over the last months have been successful in many other ways, in preventing attacks," Langton said.
Analysts say it's too early to conclude that Britain already has a fully developed terror network. But some -- like London-based security consultant Crispin Black -- say it's fairly obvious the bombers had access to expertise, probably from overseas.
"I don't accept the story that these [young men] would spontaneously turn into suicide bombers and carry out a do-it-yourself operation in London. I think they have technical support from a bomb maker, and command and control [links] from someone else," Black said.
It is still a mystery who the mastermind -- this "someone else" -- might be. Police are working furiously to try to find fresh links which will take them further up the chain to the ringleaders.
A neighbor of one of the suspects said that the suspect told him he had recently visited Afghanistan and Pakistan.
And security sources have said there could be a North African connection, as there was in the Madrid bombings last year.
One group that lives in fear because of the terror attacks is Britain's Muslim community, whose members feel they will be blamed collectively for the atrocities.
Assistant police commissioner Andy Hayman came to the defense of Muslims at a press conference yesterday in London.
"No one should have any doubt that the work last Thursday is that of extremists and criminals. So, that being the case, no one should smear or stigmatize any community with these acts," Hayman said.
Nevertheless, a spokesman for the Muslim Council of Britain, Inayat Bunglawala, says the millions-strong Muslim community has watched unfolding events "with anguish, with shock and with dread."
"These bombers obviously thought they were doing something very meritorious by killing all those innocent people, and questions do need to be asked, questions as to what motivated them. We know that the overwhelming majority of Muslims regard the bombings with horror and revulsion,” Bunglawala said.
Bunglawala said Britain's Muslim community needs to face up to the fact that these perpetrators were Muslims, and they need to realize that these people are motivated by hatred, rather than the faith of Islam.
He also says it needs to be determined what factors could have caused such bitterness as to turn people against their fellow Britons.