North East Lincolnshire Council found over 150 of the 274 families or individuals assessed as homeless or threatened with homelessness between October and December last year needed additional assistance – most commonly for mental illness.
Of those households, 13 had more than three support needs identified.
Across England, more than 62,000 households were found eligible for statutory homelessness support – and more than half of them also required help in other areas.
Housing charity Crisis said pandemic measures had not done enough to protect those with multiple needs as Government figures show disabled people, abuse victims, care leavers and veterans were among those without a stable roof over their heads.
At 55%, Ministry of Housing, Communities and Local Government figures show that the percentage of homeless or at risk households in North East Lincolnshire last winter with one or more support needs was down from 59 per cent in the same period of 2019.
Nationally, the proportion increased from 48 per cent to 51 per cent.
While there was a slight rise in homelessness overall, pandemic measures introduced by the Government and local authorities contributed to a drop in the number of households threatened with homelessness.
Crisis chief executive Jon Sparkes said preventative policies meant fewer people had lost their homes but added: "As these figures also make clear, the action taken over the last year has not been enough to support people with multiple needs from the trauma of homelessness.
"Whether fleeing an abusive partner or experiencing mental health issues, the pandemic has made many people's living situations impossible and reduced their options."
More than 15,000 households assessed across England last winter were classed as having extra support needs because of mental illness, with physical disabilities and domestic abuse the next most common reasons for requiring more assistance.
North East Lincolnshire council found 40 households needed support linked to mental illness, 24 because of physical needs or disabilities and 24 due to domestic abuse.
An MHCLG spokesman said that the Homelessness Reduction Act allowed councils to refer people to additional support services where necessary and said many of those in need of support are treated as a priority for homelessness assistance.
He said: “We know that many people experiencing homelessness or rough sleeping have additional support needs and the reasons that someone may become homeless are varied and complex.”
The Government will spend £52 million this year on specialist substance misuse services for those sleeping rough or in emergency accommodation, while 2018/19 saw funding granted to 47 authorities to help care leavers at risk of homelessness.