Lord Dyson, Master of the Rolls, said the legal challenges were to two "of the Government's most controversial measures" relating to state benefits.
The court could only intervene if the measures "were manifestly without reasonable foundation", the judge said.
He ruled that the test was not satisfied and both challenges must fail.
Representatives for two of the people with disabilities who lost their bid said they were "extremely disappointed" and "baffled" by the court's findings.
"We are currently considering whether an appeal to the Supreme Court is possible" said Ugo Hayter, from law firm Leigh Day.
More top news
Building officials reportedly ordered occupants to evacuate after the fire broke out.
Arsenal have completed the signing of Spanish forward Lucas Perez from Deportivo La Coruna.
A stunning afternoon ahead with near unbroken blue skies and warm sunshine for many of us.