In a report measuring improvements in child health, the Royal College of Paediatrics and Child Health (RCPCH) says that it is "disappointed and gravely concerned" by a lack of progress by the government in reducing child poverty and tackling inequality, which are indicators of poor health.
The RCPCH says that falls over the last 100 years in infant mortality have stalled and could be "catastrophic" by 2030 unless progress is made.
The UK's impending exit from the European Union (EU) is another threat to child health as it threatens to undermine access to medicines, treatments and investment in research, adds the report.
The government is being called on to ensure that investment in child health research is a priority as Britain leaves the EU.
Also being called for is for the adoption of a "child health in all policies" approach across government. In particular, the RCPCH wants the Treasury to disclose information about the impact of the Chancellor's annual budget statement on child poverty and inequality.
Cuts to public health funding is another issue raised in the report. It points to King's Fund analysis that shows that councils were projected to spend £2.52bn on public health services in 2017/18, compared with £2.6bn the previous year. Being called for is an end to public health funding cuts until the effects of such cutbacks are analysed.
Health visiting and school nursing services should also be handed extra money, especially in supporting children living in poverty, says the report.
A particular concern raised is a drop in health visitor numbers, from 9,491 to 8,588 between 2016 and 2017.
Despite the concerns the report praises progress in some areas of child health since it produced its first State of Child Health report in 2017.
The royal college welcome a strategic focus on improving children's health outlined in the Long Term Plan for the NHS. The government's prioritisation of children and young people's mental health and obesity over the last year is also welcomed.
"We are witnessing a hugely welcome shift towards the prioritisation of child health, which is exciting for the health prospects of children today and generations to come," said RCPCH president Russell Viner.
"But there are significant risks on the horizon. The political uncertainty caused by Brexit looms large, raising legitimate concerns about recruiting enough children's doctors and nurses and access to medicines and to EU funding for vital child health research.
"Government must act now to ensure a focus on the children's workforce and investment in child health research are prioritised to mitigate the potentially damaging impact of Brexit."
He also warned that inequality could "undo much of the progress".
"Deprivation is a major contributing factor to poor child health outcomes, and can lead to higher rates of poor mental health, increased alcohol or substance misuse, obesity, and death," he said.
"Babies from the most deprived families are also more likely to be born premature or a low weight which makes them more susceptible to illness.
"The gap between rich and poor continues to widen so without inequalities being addressed, England has little chance of catching up with its European neighbours."
A Department of Health and Social Care spokeswoman said: "As this report makes clear, the mental and physical health of our children and young people is a key priority for this government.
"That's why the NHS Long Term Plan has committed to prioritising prevention so children can live well in their communities, increasing funding to give 345,000 more children and young people access to NHS-funded mental health services, as well as earlier detection and cutting-edge treatments for major illnesses, including genomic tests for every child with cancer."