The Government has a commitment to bring particularly vulnerable accompanied children into the UK, under the Dubs amendment to the Immigration Act.
But the Home Office has failed to provide sanctuary to the most at-risk refugee children and not given proper written decisions in refusing these applications, their lawyers say.
It was revealed in early December that hundreds of children who had expected to come to the UK had been refused asylum by the Home Office.
Charities have previously taken legal action against the Government over its handling of minors asylum claims. But this will be the first time that children have launched their own individual cases.
Of the 36 bringing the action, 28 have already had their asylum cases refused, while another eight are still waiting for a decision from the Home Office, The Guardian reported.
Toufique Hossain, director of public law at Duncan Lewis Solicitors, told the paper: The Government has rendered these children, including some as young as 13, to effectively be without any legal remedy until well into the new year, which is the earliest that the relevant Home Office officials have agreed to give reasons for refusing some of these children.
He added: The way that this has all been handled by both the UK and French authorities is nothing short of shameful.
It is morally reprehensible and, we argue, simply unlawful that these children have not been given written reasons as to why their applications were refused and that these children were told about the refusals in group meetings without a proper procedure in place.
The Home Office also faced criticism last month when it published guidelines restricting the children who would qualify to come to the UK under the Dubs amendment.
Under new eligibility criteria, a child must be 12 or under unless they are either Syrian or Sudanese. Then they can be 15-years-old.
Their siblings, if under the age of 18, also qualify as do those at high risk of sexual exploitation,
Labour peer Lord Dubs, who fled the Nazis and came to Britain as part of the Kindertransport scheme, has said the recent changes to the criteria were shocking.
I think in those new eligibility criteria they have breached both the letter and the spirit of the amendment, he said. I think they have gone back on their word.
A Home Office spokeswoman said: It would be inappropriate to comment on ongoing legal proceedings.