The UK's terror threat level has been lowered from 'critical' to 'severe', the British Home Secretary Amber Rudd has announced.
It means an attack is considered highly likely rather than imminent.
The level had been raised on Friday to the highest - critical - following the bucket bomb blast at Parsons Green Tube station that left 30 passengers injured.
Troops were deployed to key locations so armed police were freed up to patrol the streets.
Two people have been arrested in connection with the west London bombing, and Ms Rudd has announced the UK threat level was being downgraded.
"I would urge everybody to continue to be vigilant but not alarmed," she said.
"During the next few days, the military will return to their original positions.
"I'd like to take this opportunity to thank them for their hard work, and also the police, the security services and the emergency services who did such a fantastic job."
She added that the Joint Terrorism Analysis Centre (JTAC), which sets the terror threat level, had decided "sufficient progress has been made" to lower it.
But she warned the Parsons Green investigation was "still an ongoing operation".
Assistant Commissioner Mark Rowley, who is the UK's most senior counter-terrorism officer, also announced that police were "getting a greater understanding of the preparation of the device".
He confirmed more police - some armed - would remain in place on the streets and transport networks at the beginning of the week.
Arrests
The announcements come after two men were being held in connection with the Tube blast.
An 18-year-old was arrested at Dover ferry port on Saturday morning and a 21-year-old was arrested at a fried chicken shop in Hounslow on Saturday night. Neither have been named.
Police searched what is believed to be the 21-year-old's home in Stanwell, Surrey, on Sunday.
He and the other man are being questioned by police on suspicion of offences under the Terrorism Act.
Leader of Spelthorne Borough Council Ian Harvey said the 18-year-old is understood to be an Iraqi orphan who had moved to Britain when he was 15.
Both men are believed to have spent time in the care of Penelope and Ronald Jones, who received MBEs for services to children and families in 2010.
They have been highly respected foster parents for almost 40 years and looked after up to 300 children, including eight refugees.
Mr Harvey told the Press Association: "One thing I understand is that he (the 18-year-old) was an Iraqi refugee who came here aged 15 - his parents died in Iraq."
Of the other suspect, he said: "I think it is widely known that this person who lives at (the Stanwell) property was a former foster child at the property which was raided."
Mr and Mrs Jones's home in Sunbury on Thames was searched by armed police on Saturday morning and is still being examined by counter-terrorism investigators.
Footage has emerged of a man in Sunbury carrying a Lidl bag, similar to the one the suspected device was hidden in, around an hour and a half before the attack.
The man was seen on camera at 6.50am reportedly leaving a house which police would later search.
Meanwhile, all but one of those injured in the attack have been able to leave hospital. As well as injuries from the fire, many people were hurt in the stampede of passengers trying to escape the bomb.
