Tragic little Freddie Neil was found lying on the floor in his older brother”s room and pronounced dead on arrival at hospital.
His parents Matthew Neil and Kim Smart-Neil were arrested and charged with neglect and manslaughter.
But the CPS later decided to drop charges after deciding there was not enough evidence.
Details of the baby”s shocking death have been revealed after a serious case review.
It found how his mother and father spent the 24 hours beforehand downing “a large quantity of alcohol” in a pub and with friends at their home in Blackpool, Lancashire.
The mother, aged 32, last remembered attending to Freddie around 5am and her husband, a local DJ, stayed up with the baby until around 6am when their friends left.
An inquest heard that Neil, 34, who was “extremely tired and intoxicated”, remembered taking Freddie to bed but could not say how he came to be in their other son Alex”s room.
He was woken around noon the following day, Boxing Day, by Alex crying at the stair gate with his nappy off and excrement on the floor.
Neil, who had turned down help for alcoholism weeks earlier, changed Alex”s nappy before noticing Freddie was not in his basket.
After searching the house, he then found him unresponsive and partially wrapped in blankets on the floor between a wall and bed in Alex”s room but neither parent could say how he got there.
The father tried CPR but the baby was pronounced dead after being taken to Blackpool Victoria Hospital.
Coroner Alan Wilson, who recorded an open verdict, heard that Freddie had bronchitis and it was impossible to say what exactly caused his death.
A pathologist said she believed his death was caused largely by unsafe sleeping arrangements.
Neil denied being drunk and said he remembered putting Freddie to bed in his Moses basket, but admitted he did not know how he ended up in a different room.
Speaking after the report findings, the father said: “It was Christmas and we both had more than we should”ve, but neither of us was inebriated.
“I believe I had a fit. There”s no way a four-week-old baby can make it from our room into Alex”s room on his own. It”s a sheer impossibility.
“One of us had to have moved him but when I have a fit I can”t remember half an hour before or after.
“I can”t remember taking him in there, so that”s the most viable explanation. It”s the most sensible one.”
Neil, who was found to be twice the legal drink drive limit, and his partner were arrested on suspicion of neglect and manslaughter, but were released without charge in June.
The report by the Blackpool Safeguarding Children Board also found there was nothing authorities involved with Freddie”s family could have done to prevent or predict his death.
Neil was an “admitted alcoholic” who told hospital staff he was drinking “seven plus pints per day”.
It found alcohol was a feature of Freddie”s short life but said there was no evidence it posed a problem until that night, with his parents providing a “relatively safe environment”.
Neil twice turned up at Alex”s nursery smelling of alcohol during Freddie”s short life, although staff did not believe him to be “under the influence”, the report said.
He did not seek help from drug and alcohol services until after Freddie”s death despite advice from his GP, it added.
The CPS said: “We considered the criminal charge of wilful neglect and the file was carefully reviewed according to the Code for Crown Prosecutors.
“The CPS concluded, following consultation with the investigating police officers, that there was insufficient evidence to charge either person with this offence.”
The serious case review was carried out by Amanda Clarke who probed the services involved with Freddie”s family, including their GP and nursery, the ambulance and midwifery service, and health visitors.
She made a number of recommendations on how to prevent further deaths of this nature.
They include launching a campaign to warn of the dangers of drinking alcohol while looking after children, improving assessments to identify families” needs, working with expectant and new fathers to offer advice and support, and introducing a compulsory safe sleep assessment to be carried out by health professionals.
Blackpool South MP Gordon Marsden said: “This is a poignant case which highlights the need for improved family support particularly when different stresses produce a tragic cycle of events.
“Neither the coroner nor the detailed review which followed Freddie Neil”s death found it possible to ascribe a simple cause and nor do I think would I.”
The NSPCC said: “Children who parents have alcohol problems can often be at most risk of harm, as this tragic case starkly illustrates.
“It”s crucial for these parents to seek help and support to develop healthy and secure relationships with their children.
“The NSPCC runs a specialised programme called Parents Under Pressure, which helps parents manage their alcohol problems and so create a safer family environment.”