British Prime Minister Theresa May has vowed to get tough on terrorism, after seven people died and more than 40 were injured when three men mowed down pedestrians on London Bridge before going on a stabbing spree.

After chairing an emergency security meeting yesterday morning, she said "enough is enough", and that the country cannot pretend that things can continue as they are.

The government will review anti-terror laws to give police more powers and stiffen punishment for terror-related offences, step up efforts to prevent radicalisation, and cooperate with other governments to get Internet companies to stem the spread of extremist ideas.

Yesterday, police arrested as many as 12 people after raiding a property linked to one of the attackers in Barking, east London, as they frantically try to piece together a picture of the three men.

The trio went on a rampage last Saturday night in one of central London's busiest areas, as revellers packed the many restaurants and bars in the iconic Borough Market next to London Bridge.

A white hire van careened at high speed into pedestrians along the bridge at 9.58pm before the trio, wearing fake bomb vests, jumped out and started slashing people with 30cm blades. Witnesses said they heard the men shouting, "This is for Allah", as they cut down terrified revellers. Some people hurled chairs, bottles and glasses at the attackers to stop them.

Police arrived and shot dead the three assailants within eight minutes of getting the first call, drawing praise for their swift response.

Metropolitan Police Assistant Commissioner Mark Rowley said eight armed police officers fired an "unprecedented" 50 rounds to stop the attackers. He said police were making significant progress in identifying the men, but gave no details.

During the attack, many people took refuge in restaurants in the area, which went into lockdown.

Singaporean Ellen Chew, 48, who owns a tapas restaurant, Lobos, at Borough Market on the main street, said people ran into the restaurant to hide. She was not there when it happened but she said her employees were "quite distraught".

"We are all saddened by this senseless tragedy, especially since it happened on home ground, and we want to help the people affected, where possible," she said.

The attack came just a night before a benefit concert in Manchester held by pop singer Ariana Grande and others to pay tribute to the 22 people, including children, who died when suicide bomber Salman Abedi blew himself up at the end of her concert less than two weeks ago.

Last Saturday's attack is the third terrorist strike in Britain in about three months, including the Westminster Bridge attack on March 22 that killed five people when a British-born man rammed his car into pedestrians on the bridge leading to the Houses of Parliament.

The country's threat level was raised from severe to critical for five days after the Manchester attack, over fears that Abedi had other accomplices or had built other bombs. Members of the intelligence community at yesterday's emergency meeting recommended against raising the terror alert again, which meant they did not believe other terrorists are at large.

But there is fear that the London Bridge incident will inspire copycat attacks, just as it might have been influenced by the Manchester attack. There is also worry that there will be more terror incidents during this holy month of Ramadan, when extremists have been encouraged to wreak havoc.

After the latest attack, major political parties yesterday suspended national campaigning for the general election, which takes place on Thursday.