'Large part' of Manchester attack network held in UK
Nine suspects are currently in detention on UK soil in connection with the blast, for which the Islamic State group has claimed responsibility.
Police in Libya have meanwhile detained the father and brother of 22-year-old bomber Salman Abedi.
Mark Rowley, head of the UK's counter-terrorism unit, said police had got hold of "a large part of the network" linked to the atrocity in which seven children aged under-18 were among the 22 dead.
"We are very happy we've got our hands around some of the key players that we are concerned about but there's still a little bit more to do," he said.
Police said the nine men in custody ranged in age from 18 to 44, including a 30-year-old arrested in the Moss Side area of south Manchester early on Friday and a 44-year-old detained in nearby Rusholme later in the day.
"I woke up because I heard the police shouting, they were shouting 'Get down, it's the police, hands on the ground, get on the ground'," said local resident Anita Santonelli, who said she saw around 10 armed police officers during the morning operation.
Meanwhile, opposition Labour leader Jeremy Corbyn said it was the "responsibility" of governments to minimise the risk of terror by giving police the funding they need after cuts made while Conservative Prime Minister Theresa May served as interior minister.
Following Monday's attack in which 116 people were also injured, May and Corbyn suspended campaigning for a snap 8 June election.
|We take full responsibility for that and obviously regret that that happened.|
Meanwhile, the top diplomat Rex Tillerson also visited London on Friday in an expression of solidarity after Britain reacted furiously to leaks of sensitive details about the investigation emanating from Washington.
"We take full responsibility for that and obviously regret that that happened," the secretary of state told reporters.
The UK briefly suspended intelligence-sharing with the US over the leaks, but Tillerson said their "special relationship" would "withstand this particular unfortunate event".
President Donald Trump has threatened to prosecute those responsible for the "deeply troubling" security breach.
Monday's bombing at a concert by US pop idol Ariana Grande was the latest in a series of IS-claimed attacks in Europe that have coincided with an offensive on the militant group in Syria and Iraq by US, British and other Western forces.
Dozens of IS fighters were killed in US strikes on Syria Friday, while masked gunmen killed at least 28 people in an attack on Coptic Christians in Egypt.
Britain's terror threat assessment has been hiked to "critical" - the highest level - meaning an attack is considered imminent.
The issue of security, which was not widely discussed in the general election campaign before the attack, is now expected to feature highly.
A YouGov poll in The Times newspaper put the Conservatives on 43 percent compared to Labour on 38 percent, far better for Labour than the double-digit margin that had previously separated it from the governing party.
However, the poll also suggested that 41 percent of respondents believe the Conservatives would handle defence and security best, compared to 18 percent who said the same of Labour.
YouGov polled 2,052 people on Wednesday and Thursday.