No troops are expected to be deployed onto the streets following the London terrorist attack.
Three men were shot dead after killing seven and injuring 48 more with a van and knife attack around London Bridge and Borough Market.
The Home Secretary, Amber Rudd, says there are no plans to raise the terror threat level back to 'critical'.
It was raised to the highest level - which means further attacks are imminent - following the Manchester Arena atrocity.
The official terror threat level in the UK was returned to severe, the second-highest category, early last week.
Ms Rudd told ITV's Peston on Sunday programme:
"The critical level went up because in Manchester we had to be... absolutely sure that there was no additional material or explosives out there that could mean there might be a follow-up attack."
"When they became satisfied of that the independent assessor of the threat level, the Joint Terrorism Analysis Centre (JTAC), said it was right to come back down to severe.
"We don't believe there is [sic] additional elements which could be carrying on the attack we saw last night... JTAC has made that assessment. So they haven't recommended going to critical".
When JTAC moved the terror threat up to critical following the Manchester Arena attack, it triggered heightened security measures including the deployment of military personnel to support police under Operation Temperer.
Scotland Yard head Cressida Dick said police believe there were three attackers and that all have been "neutralised".
Ms Dick said authorities are already at a "very high level of alertness".
A large cordon remains in place in the affected areas as officers conduct searches to ensure there are no suspects outstanding.
Ms Dick said:
"We don't believe there is but we must make absolutely certain ... and as I said we have a very large investigation ongoing and we will be seeking to establish whether anyone else was working with or assisting in any way, or helping in the planning of this attack in the way that you would expect."
Police have said a benefit concert for the Manchester bombing victims will still take place but security will be stepped up.
Assistant Chief Constable Garry Shewan from Greater Manchester Police said:
"We're deeply saddened to hear about last night's horrific attacks in London and our thoughts are with everyone affected, including the emergency services responding to the incident.
"There are two large-scale events taking place in Greater Manchester today and we would like to assure people that these will still take place, but with additional security in place to ensure the safety of everyone."
"We have dedicated resources at both events, with a significant number of officers from both GMP and colleagues from other forces, some of which will be armed.
"There will be additional security checks taking place and everyone will be searched, including bags. We would ask people not to bring bags if they can, as this will help speed up entry.
"I'd like to remind people that the threat level remains at severe, which means an attack is highly likely."
Cover photo courtesy of SWNS.