British Prime Minister Theresa May said Saturday morning that the country's terrorism threat level has been reduced from its top level of "critical" to "severe".
Troops to bolster police numbers will be gradually withdrawn from the streets starting Monday, May said.
Greater Manchester Police had arrested another man overnight on suspicion of terrorism offences as part of its ongoing investigation into the attack.
The level was raised to "critical" - meaning another attack was thought to be imminent - after Monday's bombing at a pop concert in Manchester.
Theresa May said the decision followed a "significant amount of police activity over the last 24 hours".
It had been set at critical in the aftermath of the Manchester bombing. "A threat level of severe means an attack is highly likely", she said.
Greater Manchester Police said the adjusted terror threat level will not affect its investigation, with the force stressing "the level of resources we have available to us remains the same".
In the latest police action on Saturday, officers used a controlled explosion to gain entry to an address in the north of the city where two men were detained.
"As part of an ongoing search at a property in Moss Side an evacuation is now being carried in the area", police said in a statement.
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"All of this is created to make the policing approach unpredictable and to make London as hostile an environment as possible to terrorists", said Chief Superintendent Jon Williams of London's Metropolitan Police Service.
The Times newspaper said on Saturday that intelligence officers had identified 23,000 jihahist extremists living in Britain.
Security is being increased at football cup finals at Wembley Stadium in London and the Great Manchester Run.
The evacuation was described by Greater Manchester Police as a precautionary measure to "ensure everyone's safety".
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.
"We can't directly link these to the events of Monday night and are continuing to monitor the situation", he said.
May said Labour leader Jeremy Corbyn was saying Britain was to blame for the bombing.
A poll on Thursday put May's Conservatives five points ahead of Labour suggesting a far tighter race than previously anticipated.