The government has lowered the terror threat level for the UK from "critical" to "severe".
The announcement comes after multiple arrests and home raids were carried out during the weekend, first in Dover and later in west London .
Home Secretary Amber Rudd said police had made "good progress" in the investigation of the Parsons Green terror attack as she announced the reduction of the highest possible threat level.
Ms Rudd said:"The joint terrorist analysis centre, which reviews the threat level that the UK is under, has decided to lower that level from critical to severe.
Parson Green Terrorist incident
"Severe still means that an attack is highly likely so I would urge everybody to continue to be vigilant but not alarmed.
"Following the attack in Parsons Green last Friday (September 15) the police have made good progress with what is an ongoing operation."
The announcement on Sunday (September 17) comes after police arrested an 18-year-old near Dover ferry port just one day previous.
The same day, a residential Address in Sunbury was searched by armed police officers.
A residential address in Stanwell , Surrey, is now being searched in connection with the arrest, Scotland Yard said.
The Home Secretary said it appears the bomber was not a lone wolf but added it is "too early to reach any final conclusions on that".
When asked if she could give any information on claims by Islamic State that there were other unexploded devices, she told BBC's Andrew Marr Show: "We don't.
"It is inevitable that so-called Islamic State, or Daesh, will reach in and try and claim responsibility.
"We have no evidence to suggest that yet."
Following the arrests, Assistant Commissioner Mark Rowley said police were gaining a "greater understanding of the preparation of the device".
He said: "The high pace and rapid progress of this investigation is continuing.
"There was another arrest overnight and two men are in custody. There are now two searches continuing at addresses in Hounslow and Surrey and we are getting a greater understanding of the preparation of the device.
"There is still much more to do but this greater clarity and this progress has led JTAC - the independent body that assesses threat - to come to the judgement that an attack is no longer imminent."
Speaking about the police presence in London, he added: “For practical and precautionary reasons we made the decision that the increased resources will continue for the beginning of this week.
“So the public will still see that high level of policing presence; some armed, some unarmed.
“The military support we have had in place under Operation Temperer will start to phase out as we move through the coming week."
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