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
Fans around the globe have been celebrating Pac-Man's 35th anniversary by paying homage to the smiley faced character.
Sir Ian McKellen has revealed he was in "two minds" about accepting his knighthood as he thinks the honour system is unfair.
Harlem Globetrotters legend Haynes has been hailed as "a pioneer" who helped "set the tone for modern basketball", following his death.