In a separate statement, Lissie Harper, PC Harper’s widow, said it was “disgusting” that his killers could be eligible for early release.
She said she was “beyond appalled and bristling with anger to hear that Andrew’s killers are soon to be free to roam the streets”.
Thames Valley Police Chief Constable Jason Hogg said the decision not to exclude them was “demoralising for all police officers”.
The Sentencing Act was amended in January, with the eligibility for early release based on the length of fixed sentence, rather than the type of offence.
The act already excluded some of the most serious and dangerous offenders, such as murderers serving life sentences or those on extended sentences.
But last month, Burnham paused the plans after backlash from survivors. The scheme will now restart in October.
Announcing the changes on Monday, he said: “I fully understand the anger, anxiety and distress that’s been caused. I’ve heard that loud and clear.”
Under the revised plans, rape and child sexual offences will now also be excluded from early release.
The government also announced an extra £10 million will go to front-line victim support services, including a new national helpline.
This move does not require changes to the existing legislation before October, the government said, though it may make amendments in the future to exclude certain offenders from being released.
Offenders of other crimes serving longer sentences of four years or more will be eligible for release halfway through their sentences rather than two-thirds as had previously been the case.
Those serving less serious sentences could be freed after a third of their time, rather than half.
The changes are due to be phased in, beginning with prisoners serving sentences of less than 575 days, going up to inmates jailed for 12 years or more being eligible for early release in June 2027.
The “presumption” will be that offenders are tagged and will face longer periods of supervision and tough new rules including “restriction zones”, Burnham said.
The number of individuals released each time will depend on the make-up of the prison population, which the government says will evolve between now and implementation.