The report recommends using NHS apps to improve the experience of booking jabs, investing and expanding vaccination services, and funding health visitors to deliver some of them.
It also calls on the development of the 'digital red book' to be finalised so parents can keep track of their children's vaccinations.
The NHS website lists the full schedule of vaccinations for children, from babies, up to the age of 15.
Dr Julie Yates, deputy director for immunisation programmes at UK Health Security Agency, said plans were in place to improve childhood vaccine uptake by ensuring more flexible appointment booking systems, making vaccines more widely available across different locations, and making access easier in all communities.
"Despite the challenges, it is also important to note that parents have high confidence in vaccinations with almost 90% agreeing vaccines are effective," Dr Yates said.
Alison Morton, chief executive of the Institute for Health Visitors, said the report presented "a compelling case" to ensure babies and children are protected against serious diseases which can cause so much unnecessary harm.
Helen Bedford, professor of children's health at University College London, said improvements needed investment in staff and infrastructure.
"Our children have the right to be protected from preventable diseases which can cause illness, disability or even death," she said, adding that a fall in children getting their vaccines had resulted in the deaths of 11 young babies from whooping cough last year.
Falling vaccinations among children isn't just an issue in the UK, in 2023 there were nearly 16 million children who had not had any vaccinations, most of them in south Asia and sub-Saharan Africa.