An archbishop has called a terrorist attack in London in which three people were stabbed "saddening and shocking."

Archbishop John Wilson of Southwark lamented how "yet again" innocent bystanders had become victims of terrorist violence. One of those stabbed was a Catholic preschool teacher.

In a statement issued shortly after Sudesh Amman was shot dead by plainclothes police after embarking on a stabbing spree, Archbishop Wilson declared: "Violence solves nothing.

"It is both saddening and shocking that, yet again, there has been a terrorist attack on innocent bystanders on a street in London," said Archbishop Wilson.

"A normal Sunday afternoon in Streatham became the scene for a violent attack," he said in the statement posted on the website of his archdiocese, which includes London south of the River Thames.

"For those who think that terrorism can achieve anything, we commit ourselves with determination to saying 'no' to violence on our streets and within our communities," he continued, offering prayer for the injured, their families and for emergency services personnel.

He noted that Londoners were from different countries and had religious beliefs, "but we are united in our common humanity and our shared desire for a peaceful coexistence where every person is respected and can live in safety."

Ten days before the attack, Amman, 20, had been released on probation, halfway through a 40-month sentence for possessing and distributing terrorist documents. He was considered to be so high risk that he was under 24-hour surveillance by a team of more than 20 police officers.

But on the afternoon of Feb. 3 he donned a fake suicide vest and stole a 10-inch knife from a store and immediately used it to attack three passers-by before he was shot by undercover officers.

British media identified one of his victims as Polish-born Monika Luftner, 51, who teaches at a Catholic preschool in London. The Sun newspaper reported Luftner was knifed in the back as she cycled in Streatham shortly after dropping off her 12-year-old daughter with friends.

Luftner is now making a "good recovery" in the hospital. A man, who has not been identified, is also recovering in the hospital from his injuries, while a third victim was sent home.

The attack came just two months after convicted terrorist Usman Khan stabbed two people to death near London Bridge.