Mr Street made the request to Attorney General Suella Braverman, saying the sentence did not match the "seriousness" of the crime.
Davis killed 18-day-old baby Ciaran Morris after crashing his BMW into a pram on Brownhills High Street on Easter Sunday last year, before he fled the scene.
Jurors at Wolverhampton Crown Court on April 8 found the 35-year-old guilty of causing death by dangerous driving and also causing death while uninsured.
Davis, from Croxtalls Avenue in Bloxwich, was jailed for six-and-a-half years and banned from driving for seven years and three months.
Now the Mr Street has written to Ms Braverman, calling for the sentence to be referred to the Court of Appeal where a harsher sentence could be imposed.
In his letter, Mr Street said: "We are writing to ask you to review a sentence which we believe is unduly lenient, handed down to a driver who killed a two-week-old baby.
"Rather than going down for a long time, however, he was jailed for just six and a half years. The defendant pleaded not guilty throughout and before sentencing, it was revealed Davis had made 11 previous court appearances for 35 offences including driving without insurance in 2003, twice in 2004 and again in 2006, drug dealing, driving while uninsured, drink-driving and theft of a vehicle.
"The current maximum sentence for causing death by dangerous driving is 14 years and this would appear to be one of the most abhorrent examples resulting in the killing of an 18-day-old baby.
"We feel Davis' sentence does not match the seriousness of the crime and the wilful disregard for people's safety shown during previous offences. The previous convictions, the serious injury caused to Ciaran's mother, the other offences commitment at the same time (driving without insurance) and the attempt to avoid detection should place this at 'level one' (the most serious) under the sentencing guidelines."
The letter, also signed by West Midlands Cycling and Walking Ambassador Adam Tranter, called for a harsher driving ban – a potential lifetime ban – to be imposed on Davis due to his previous convictions and this offence.
It said: "Alongside a custodial sentence, given the defendant's prior driving history including multiple convictions for drink driving, we also fail to see how James Davis should ever be allowed to drive again. However he has only been banned from driving for seven years and three months.
"To make our roads safer, we need to make driving bans serious. Of the 63,342 driving bans given at court in England and Wales in 2018, only five were lifetime bans – approximately one in 12,500.
"We have copied this letter to the Home Secretary and Transport Secretary as we believe the length of driving bans on the whole needs to be urgently addressed. Here in the West Midlands, we're committed to improving road safety but as a part of that, the justice system needs to provide a meaningful deterrent against the illegal behaviour of some drivers.
"We would therefore ask you to please refer this case to the Court of Appeal as we believe it to be unduly lenient under the current guidelines."
The call for a review has been backed by Councillor Stephen Craddock, who represents Brownhills, who called the sentence an "absolute disgrace" – with Davis potentially freed sooner if he has good behaviour in prison.
Councillor Craddock, speaking to the Express & Star, said: "I think it's an absolute disgrace he got six and a half years for this. He has served a year on remand and he could be free in just over two years, with a 50 per cent discount, it doesn't seem equitable.
"And the driving ban doesn't seem to make any sense at all, he is a serial offender who knew what he had done. The man is a disgrace – he should have received near the maximum sentence of 14 years for this."
The Brownhills representative added he "sincerely" hoped the case would be reviewed and Davis would be handed the tougher sentence, and a lifetime ban from driving.