The attacker, Usman Khan, was convicted on terrorism-related charges in 2012, and had been released from prison previous year.
"We've taken a lot of action as you can imagine in the last 48 hours".
In his address Sadiq Khan said that London would never be intimated by terrorism.
Hussain is supposed to have been Khan's close friend, although police said there was no information linking him to the London Bridge attack.
"There are enormous questions to be learned from this bad event that happened last week and that is: What happened in the prison with this particular individual, what assessment was made of his psychological condition before he was released, and also what supervision and monitoring he was under after coming out?" said Corbyn.
He penned an article setting out the new stance in The Mail on Sunday newspaper, under the headline: "Give me a majority and I'll keep you safe from terror". "Our thoughts and prayers are with the families of Jack Merritt and Saskia Jones, and all those injured or affected by the attack on Friday".
"Jack lived his principles; he believed in redemption and rehabilitation, not revenge, and he always took the side of the underdog", the statement said. They said he "would not want this bad, isolated incident to be used as a pretext by the government for introducing even more draconian sentences on prisoners, or for detaining people in prison for longer than necessary". The 25-year-old was a Cambridge graduate and Course Coordinator for the University's Learning Together Programme.
Corbyn said Conservative cuts to community policing, probation, mental health, youth and social services could "lead to missed chances to intervene in the lives of people who go on to commit inexcusable acts".
Two of the three people injured in the attack remained hospitalized in stable condition.
The early assessment is that Khan was acting alone and wore a hoax suicide bomb vest because he wanted to be shot.
A book of condolence is to be opened for victims of Friday's attack on London Bridge.
But the Islamic State group has released a statement claiming responsibility for the attack.
Lukasz, who was working in the basement of the Fishmongers' Hall when Khan carried out his deadly attack, rushed to help stop the terrorist.
All nine jihadists were members of an al-Qaeda-inspired cell which plotted to blow up the London Stock Exchange and kill Boris Johnson.
Jones's family also highlighted her dedication to criminal justice.
Labour says cuts to policing and social services under a decade of Conservative leadership have made it harder to fight militancy, to track former prisoners and to reintegrate them.
That is also the view of the main opposition Labour Party, which noted that the Conservatives have been in power for almost a decade but had chosen not to tighten the laws around terrorism sentencing.
A veteran peace campaigner, Corbyn has also said convicted terrorists should not necessarily serve their full prison terms, and has long said that British foreign policy in the Middle East has played a role in motivating militants.