His words echo comments he made after London's last terror attack at Fishmongers' Hall near London Bridge when two people were killed by convicted terrorist Usman Khan.
After that attack in November, he spoke of his anger and claimed that scrapping early release from prison would have stopped Khan's murder spree.
He said then that preoccupations with Brexit had meant the Government had been unable to make the changes required to keep violent offenders and terrorists in jail for longer.
Speaking in the wake of the London Bridge attack, he insisted the system must be changed, adding: "If you are convicted of a serious terrorist offence, there should be a mandatory minimum sentence of 14 years - and some should never be released.
"Further, for all terrorism and extremist offences the sentence announced by the judge must be the time actually served - these criminals must serve every day of their sentence, with no exceptions."
In a statement released after the Streatham attack, Mr Johnson said the Government had "moved quickly" to introduce measures to strengthen the UK's response to terrorism.
Details of the Counter Terrorism (Sentencing and Release) Bill were released last month but the bill has not yet been approved by Parliament.
They include forcing dangerous terrorists who receive extended determinate sentences to serve the whole time behind bars and scrapping early release from jail for those classed as dangerous and handed extended determinate sentences.
Terrorists deemed not to be a risk would have to serve two-thirds of their sentence before the Parole Board could consider them for release, as part of the bill.
Shortly after the December attack, Home Office figures analysed by the PA news agency showed more than 350 convicted and suspected terrorists had been freed from prison over the previous seven years.
Overall, 353 terror criminals and suspects had been released from prison between June 2012 and the same period in 2019, of which 245 were convicted of offences.