This is nearly three times the number of adults diagnosed this way which is 13%, Teenage Cancer Trust said.
Of these young people, 26% had already seen their GP with cancer symptoms.
The report shows diagnosis through A&E is associated with poorer prognosis and poorer care experience.
The figures are from the Improving Diagnosis report by Teenage Cancer Trust. About seven people aged 13 to 24 are diagnosed with cancer every day in the UK.
Siobhan Dunn, chief executive of Teenage Cancer Trust, said: "We must empower young people to be persistent at the doctors if they're not getting better and not wait until they have to go to A&E."