Fire Brigades Union general secretary Matt Wrack said:
"Firefighters at the Apollo Theatre were fantastic in their response to an incident that could have seen significant loss of life, but we're sick of being praised by politicians one minute and stabbed in the back the next.
"Our world-class fire and rescue service is being devastated by the worst cuts in our history, cuts that prevent firefighters from doing their jobs during day-to-day emergencies, major incidents like the Apollo Theatre or Clutha Bar collapses and recent floods and storms."
Boris Johnson said he was "pleased" that the court had recognised the robustness of the fire authority's plans.
"I hope that all the parties involved will now draw a line under this and help us move forward and work with the Fire Commissioner to deliver a stable and secure future for the brigade.
"London's fire-fighters are the best in the world with incomparable response times. However, we need to continue to modernise the service so that it is fully equipped for the challenges of 21st century fire-fighting.
"The London Safety Plan will ensure that there is a balanced budget for 2014/15 so that, wherever possible, compulsory redundancies can be avoided whilst keeping London safe."
The London Fire and Emergency Planning Authority said the seven councils had confirmed they will not appeal. This means the reductions in fire stations and fire appliances "will proceed as planned, on 9 January 2014."
The cuts are part of the fifth London Safety Plan, which details how the authority will deliver the capital's fire and rescue service over the next three years, and includes plans agreed in September to close the 10 fire stations.
The Apollo Theatre collapse demonstrates how dependent the safety of Londoners is on the stations that Boris Johnson intends to close. If the cuts go ahead, the mayor will end up with blood on his hands. These cuts are reckless, wrong and will jeopardise the safety of millions of Londoners: it will only be a matter of time before someone dies as a result of a fire engine failing to reach them in time. Although campaigners lost the legal case, we won the moral argument and, even at this late stage, we would urge the mayor to reconsider.
– Paul Embery, Fire Brigade Union's London Secretary
A judge rejected the councils' claim that the mayor's plans to close 10 fire stations were legally flawed for a number of reasons, including a failure to take into account the reality of increased fire risks in inner London.
Campaigners say the cuts, which involve the loss of more than 500 jobs and the axing of 14 engines, would be "reckless, wrong and will seriously endanger lives".
But Mr Justice Foskett ruled the process by which the closure decision was reached was lawful.
He said: "I appreciate that the outcome will come as a disappointment to a number of people who had hoped to see the proposed changes to the provision of fire services in their area set aside."