The youth homelessness charity's claim is based on 217 Freedom of Information request responses from English local authorities and data from the devolved nations.
Cenntrepoint estimates that in 2016/17 at least 86,000 young people sought help from local authorities due to homelessness or the risk of becoming homeless. However, 58 per cent of these 16- to 24-year-olds were turned away without any practical support. A third got a documented housing assessment and 13 per cent were housed.
The charity's research also found that the main reason young people find themselves in a housing crisis is because their families refuse to accommodate them.
Paul Noblet, head of public affairs at Centrepoint, said the findings expose the extent of youth homelessness in the UK.
"Tens of thousands of young people are asking for help, with many denied proper housing assessments and in some cases their legal right to housing," he said.
Under the Homelessness Reduction Act, which came into force in April, local authorities are now required to assess anyone who is facing homelessness and provide and record more meaningful assistance. It is expected that this new duty will see English local authorities having to assess up to 45,000 more 16- to 24-year-olds every year.
However, Centrepoint is concerned that councils will struggle to meet the new law's requirements.
"The Homelessness Reduction Act is a step in the right direction but it is absolutely vital that central government provides adequate funding to allow councils to fulfil their new duties and carry out tens of thousands of additional assessments," added Noblet.
Councillor Martin Tett, housing spokesman for the Local Government Association, said: "Local authorities do all they can to support homeless people in their communities into appropriate accommodation as quickly and as effectively as possible, but the reality is that demand for this support is growing at the same time as councils face significant funding pressures.
"Whilst they are doing all they can to help families facing homelessness it's essential that the new act's duties on councils are fully funded."
Under English law local authorities are only obliged to help young people with housing if they have "priority needs". These include dependent children, serious health conditions and pregnancy.
Centrepoint has launched its Youth Homelessness Databank to collect the most up-to-date data on the issue.