Basu, who was speaking out after 20-year-old Sudesh Amman stabbed two people in Streatham, London before being shot dead by police officers, admitted that police were struggling to keep on top of surveillance of unsafe individuals.
The bill will be introduced to the Commons on Tuesday before being fast-tracked through the Lords for Royal Assent.
Amman, who was jailed for three years and four months in December 2018, had been staying in a hostel for newly released prisoners in Streatham since his release.
Up to 20 officers would have been involved in watching Amman.
The earliest point at which offenders would be considered for release is two-thirds through the sentence, and release before the end of a sentence would be dependent on a risk assessment.
Dame Cressida added: 'I wish I could assure the public that everybody who poses a risk on the streets could be subject to some sort of thing that would stop them being able to stab anybody ever, but it is clearly not possible'.
British police are overwhelmed with suspected and convicted terrorists to track, as they simply can not keep an eye on every single extremist, says Neil Basu, senior national coordinator for counter-terrorism.
As many as 50 terrorists could be freed from jail this year, figures suggest.
Amman was freed last week from prison after serving part of his sentence for 16 Islamist-related terror offences - namely the possession and distribution of terrorist documents, Buckland said.
A Whitehall official, quoted by PA, said on Wednesday afternoon: "If the legislation is passed by February 27, we can prevent the automatic release of any further terrorist suspects who might pose a threat to the public".
The attack came just over two months after a similar incident when armed police shot dead a convicted terrorist on early release near London Bridge in the heart of the city.
He received a life sentence with a minimum term of five years in 2015.
The Government has not ruled out derogating, effectively suspending, the European Convention on Human Rights (ECHR) in order to apply the new measures.
The newspaper also reported that Atiq Ahmed, from Oldham, who was arrested after hurling abuse at staff at a school in the town and later found to have IS propaganda on his phone, is due to be released in March.
Lawyers have warned the move would open the Government up to legal challenges from those already behind bars who were sentenced under the current rules.
"What we are proposing in this emergency legislation is not to retrospectively alter offenders' sentences as they were imposed by the court", the government source said.