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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.
Five disabled tenants have lost their bid at the Court of Appeal to have the UK Government's so-called "bedroom tax" declared unlawful.
The changes were introduced last April. People living in social housing who were deemed to have a spare bedroom were asked to downsize or accept a reduction in housing benefit.
Two lone parents have lost their separate Court of Appeal challenge to the legality of the "benefit cap".
Judges rejected claims that the policy violates human rights laws and the common law because of its impact on vulnerable families.
In test cases of national importance, today's ruling at the Court of Appeal will decide whether "bedroom tax" regulations, introduced last April, are an "excessive and unfair burden" on people with disabilities, or a lawful and "integral aspect" of the Government's deficit reduction programme.
Backed by the Equality and Human Rights Commission, lawyers for five tenants are arguing that the regulations cannot be allowed to stand.
The Department for Work and Pensions rejects the "bedroom tax" tag and says the reality is a "spare room subsidy" has been removed from social sector tenants.
The change in regulations is expected to produce savings of £500 million a year, but opponents say they have had a "devastating" impact on many people and fail to reflect the actual needs of disabled people for extra space.
The Court of Appeal will rule today on the legality of the Government's so-called "bedroom tax," which campaigners say unlawfully discriminates against the disabled.
Judges will also decide in a separate case whether or not the "benefit cap" violates human rights laws and the common law because of its impact on vulnerable families.