Mark Rowley said "immense" progress had been made in the investigation into Salman Abedi, who killed 22 people, seven of them children, at a pop concert in Manchester on Monday.
"They're very significant, these arrests. We're very happy we've got our hands around some of the key players that we are concerned about. But as I say, there is still a little bit more to do," Rowley told broadcasters.
Since the attack, armed police backed up by the army have been patrolling cities and trains. Interior minister Amber Rudd said the official threat risk remained at its highest level, "critical", meaning another attack is expected imminently.
Hospitals have been warned to be ready. However, Security Minister Ben Wallace said there was no evidence of a specific threat over Britain's holiday weekend, when major events will take place including Saturday's soccer FA Cup final in London, where extra armed officers will be on duty.
As campaigning for a national election on June 8 resumed after it was suspended following the attack, the opposition Labour Party, emboldened by its rise in opinion polls, charged that Britain's foreign policy had increased the risk of attacks.
Labour leader Jeremy Corbyn also chided Conservative Prime Minister Theresa May for cutting spending on policing. "We must be brave enough to admit the 'war on terror' is not working," he said.
May hit back. "Jeremy Corbyn has said that terror attacks are our own fault," she said. "I want to make one thing very clear to Jeremy Corbyn and to you, and it is that there can never, ever be an excuse for terrorism."
May was speaking to reporters at a summit of Group of Seven leaders in Sicily where she won support for action to prevent militants from using the internet to spread propaganda.
A new poll showed Labour had closed the gap with May's Conservatives to 5 points, suggesting a far tighter race than previously anticipated.
Nine people are being held by police following the bombing at the Ariana Grande concert, including a man arrested on Friday evening. A further two people who were arrested earlier in the week have been released.
The Guardian newspaper, without citing sources, said three of the 10 people arrested so far were brothers who were believed to be cousins of the bomber. Abedi's father and two brothers have also been arrested in Britain and in Libya.
Grande, who returned to the United States shortly after Monday's attack, said on Friday she would hold a benefit concert in Manchester for the victims of the bombing.
Police hunting for the suspected terrorist network behind Abedi, the 22-year-old British-born man with Libyan parents who blew himself up as crowds left Monday's concert, were questioning the eight arrested men, aged between 18 and 38. Buildings across Manchester and northwest England were raided.
British police briefly suspended intelligence sharing with the United States on Thursday after confidential details of their investigation repeatedly appeared in US media. Tillerson said the allies' close security relationship would survive.
"We take full responsibility for that and we obviously regret that that happened," Tillerson said.
Corbyn, a veteran anti-war campaigner, said foreign policy was not solely to blame for terrorism but he would deploy troops abroad only "when there is a clear need", distancing himself from the interventionist approach that has seen Britain join the United States and other allies in military action in Iraq, Syria, Libya and Afghanistan in recent years.
"Many experts, including professionals in our intelligence and security services, pointed out the connections between wars that we've been involved in or supported ... in other countries, such as Libya, and terrorism here at home," he said.
Opponents accused Corbyn of politicising the Manchester attack. "To suggest that there is any link, that there is any justification, for the events that took place on Monday night in Manchester with UK foreign policy is outrageous," Rudd said.
She said the security services had foiled 18 plots since 2013. However, with almost 20,000 fewer police than when the Conservatives came to power in 2010, concern about police cuts is now likely to become a major issue in the election campaign.
"We're now 20,000 police officers down, and we get atrocities like this. Does the government not expect this?" one voter, who was not named, asked Rudd on the BBC's Question Time programme on Thursday night.
Corbyn promised to reverse the police cuts, many of them implemented by May in her previous role as interior minister, and said Britain could not be "protected on the cheap".
Rudd said counter-terrorism was adequately resourced, and denied the cuts had made it harder to prevent Monday's attack.
May called the snap election to strengthen her hand in negotiations on Britain's exit from the European Union. But her campaign hit trouble last week when she pledged to make elderly people pay more for their social care. She was forced on Monday to backtrack on a policy dubbed the "dementia tax" by opponents.
Support for May's Conservatives fell to 43 per cent while backing for Labour rose to 38 percent in the latest YouGov poll, helping to send sterling to a one-month low against the US dollar.
(Additional reporting by Alistair Smout, Paul Sandle, William James, David Milliken and Elizabeth Piper; Editing by Mark Heinrich)