The Royal College of Midwives has published a new position statement setting out its support for universal roll-out.
It says the boxes can be a “positive significant investment” in early years, and may contribute to reducing inequality.
Baby boxes were made available to all expectant mothers in Scotland from August last year.
In England, some NHS trusts have introduced pilot schemes or full baby box schemes over the last two years.
Wales and Northern Ireland do not have any such schemes.
The boxes, which contain essential items for newborns, are also promoted as a safe place for babies to sleep.
The RCM said provision of the boxes is likely to reduce the risks associated with unsafe co-sleeping, particularly in more deprived communities.
Co-sleeping has been identified as a key risk factor for cot death or sudden unexpected death in infancy (SUDI).
The RCM stressed that boxes must be safe, of high quality and the box and mattress should meet at least the minimum UK safety standards.
The organisation also acknowledged there is “limited evidence” around baby boxes reducing deaths from SUDI.
Earlier this year cot death expert Dr Peter Blair raised concerns about the promotion of the boxes for sleeping.
Dr Blair, chairman of the International Society for the Study and Prevention of Perinatal and Infant Death, told The Guardian newspaper: “They shouldn’t be advocating infants sleep in these boxes unless there isn’t anything else available.”
The Scottish Government said its baby box conforms to all relevant safety standards currently in place for a crib or cradle.
The British Standards Institution (BSI) is considering developing a standard specifically for baby boxes.
Gill Walton, of the Royal College of Midwives, said: “A baby box is a positive gift which signals that every baby is important and welcomed.
“Providing them will help many families whatever their background, and provide a more equal start to life for the baby.
“The Scottish baby box contains a number of very useful baby items that can support the health and wellbeing of new babies, including an electronic thermometer, a baby carrying sling, a bath thermometer and a range of clothing.
“Most importantly by enabling parents to give their babies a safe sleeping space, baby boxes may reduce unsafe co-sleeping or babies sleeping in an inappropriate place such as a sofa.”