The terror threat level now indicates that an attack remains highly likely rather than imminent. The Army troops deployed as a result of Operation Temperer will be reduced from Monday night.
Prime Minister Theresa May made this announcement after leading a meeting of the government's emergency committee Cobra this morning.
She said "significant activity" by the police during the last 24 hours led to the threat being reduced.
It had been set at "critical" in the aftermath of the bombing in Manchester.
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Earlier, a new arrest this morning has taken the total number of men being held in custody over the suicide bombing in Manchester to 11.
Greater Manchester Police had arrested another man overnight on suspicion of terrorism offences as part of its ongoing investigation into the attack on Manchester Arena on Monday that claimed 22 lives.
"As part of the ongoing investigation into the attack on Manchester Arena, two men aged 22 and 20 have been arrested on suspicion of offences contrary to the terrorism act," a Greater Manchester Police statement said.
The arrests were made after searches in Cheetham Hill area of Manchester, where a controlled explosion was used to gain entry into an address.
Greater Manchester Police had arrested another man overnight on suspicion of terrorism offences as part of its ongoing investigation into the attack.
The cousins of the bomber are believed to be among those arrested. A 34-year-old woman and 16-year-old boy who were also arrested have been released without charge.
Abedi was known to UK security services, but his risk to the public remained "subject to review", according to reports.
In the Libyan capital Tripoli, Abedi's younger brother 20-year-old Hashem and their father, Ramadan, are being held by special forces linked to the country's interior ministry.
Meanwhile, heavy armed presence is being rolled out for what is termed as a Bank Holiday weekend in the UK - an annual holiday on Monday making it a weekend packed with lots of public events.
Britain's senior-most counter-terrorism officer, Mark Rowley, had said that Scotland Yard had reviewed security at more than 1,300 events across the country and people could be "100 per cent confident" they were doing everything possible to protect them.
"Whatever events you are going to - whether you are going shopping or to sporting events or music events, I'd encourage the public to carry on. What they will see is many more police officers - some armed, some unarmed - out there to protect the public," he said.