Ms Allan said harsher sentences would give victims and the general public greater confidence in the justice system.
Her comments come after Prime Minister Boris Johnson announced the review of sentencing policy on Monday.
The work will focus on violent and sexual offenders and whether they are serving sentences that truly reflect the severity of their crimes.
It will consider whether changes in legislation are needed to lock them up for longer – by not letting them out part-way through a sentence. It will also look at how to break the cycle of repeat offenders.
Recommendations are expected to be made by the Government review team this autumn.
Mr Johnson said: "Dangerous criminals must be kept off our streets, serving the sentences they deserve – victims want to see it, the public want to see it and I want to see it.
"To ensure confidence in the system, the punishment must truly fit the crime. We have all seen examples of rapists and murderers let out too soon or people offending again as soon as they’re released.
"This ends now. We want them caught, locked up, punished and properly rehabilitated."
Ms Allan has previously raised her concerns with the Justice Minister and former Prime Minister about automatic early release for serious sexual offences. This followed the early release of former leader of a child sexual exploitation gang, Mubarek Ali.
Ali was sentenced to 22 years in prison in 2013, following a lengthy police operation. He was entitled to automatic early release on licence in November 2017, less than five years later. He was recalled to prison shortly after for breaching his licence terms.
Ms Allan said: "This announcement is hugely welcome. It shows the Prime Minister’s commitment to strengthening sentencing rules, giving victims and the public greater confidence in the justice system.
"It is wrong that offenders convicted of heinous crimes, such as Mubarek Ali, can automatically receive a reduced sentence, without even needing to go before a parole board. The Ali case made a mockery of our justice system. It undermined trust and confidence and was an insult to victims. I am so pleased to have had the platform to raise this issue in Parliament and to call for a change in the law.
"It is so welcome that the Prime Minister is listening to the concerns raised and is taking prompt action.”