Armed police will guard hundreds of events across the UK this bank holiday weekend following a reassessment of security after the Manchester bombing.
Senior officers are encouraging people to go out but to remain vigilant on the first holiday weekend with the national threat level at its highest.
Security is being increased at football cup finals at Wembley and Hampden Park and the Great Manchester Run.
Police are now questioning 11 men over the attack in which 22 people died.
The latest arrests saw police detain two men, aged 20 and 22, after officers carried out a controlled explosion to gain entry to an address in the Cheetham Hill area of Manchester in the early hours of Saturday morning.
It came after searches at a separate property in Cheetham Hill and in the Longsight area of the city.
The UK threat level was raised from “severe” to “critical” following the suicide attack at Manchester Arena on 22 May.
The country’s leading counter-terror officer, Met Police Assistant Commissioner Mark Rowley, said on Friday that “immense” progress had been made in the investigation into a suspected network linked to suicide bomber Salman Abedi.
He said there were still “important” lines of inquiry to pursue but urged the public to “go out as planned and enjoy yourselves”.
Police had reviewed security at more than 1,300 events across the country and people could be “100% confident” they were doing everything possible to protect them, he added.
“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.
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About 1,000 armed police officers have been freed up by a decision to deploy the Army to protect key sites including Buckingham Palace and the Houses of Parliament.
Policing will also be stepped up at the Aviva Premiership Rugby Final at Twickenham and the football play-offs at Wembley on Sunday and Monday.
Met Police Ch Supt Jon Williams said operations will include both high-profile and covert tactics.
“All of this is designed to make the policing approach unpredictable and to make London as hostile an environment as possible to terrorists,” he said.
He added: “Anyone coming to the FA Cup Final or the other play-off matches over the weekend will see an increase in police numbers in and around the stadium.
“At Twickenham, rugby fans will see more armed officers on foot around the stadium.”
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On Sunday, the Great Manchester Run will go ahead with runners and spectators due to turn out in large numbers as the city recovers from the bombing at the concert by the US singer Ariana Grande.
Greater Manchester Police Chief Constable Ian Hopkins has said the additional armed policing support enabled the event to go ahead.
As well as military personnel, Ministry of Defence Police are also being used to support regional forces, with Kent Police confirming that “highly-visible firearms officers are already patrolling key locations”.
Meanwhile, enhanced policing and security will also be in place at Saturday’s Scottish Cup Final at Hampden Park in Glasgow.
Supt Mark Hargreaves said: “There is no specific threat against Scotland, or the Scottish Cup Final; however, people should remain calm but vigilant and report anything suspicious to police.”
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Eleven men aged between 18 and 44 – including Abedi’s brother Ismail – are in custody on suspicion of terror offences, following arrests in Greater Manchester, Warwickshire and Merseyside.
A 44-year-old man was held on Friday evening in the Rusholme area of Manchester, with witnesses reporting seeing armed police surrounding a bus on Oxford Road.
Seven children were among those who died. A total of 66 people remain in hospital, with 23 in critical care.
Prime Minister Theresa May is to hold another meeting of the government’s Cobra emergency committee later to assess the security situation.