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 ten stations which will close on 9 January are:
- Belsize in Camden
- Bow in Tower Hamlets
- Clerkenwell in Islington
- Downham in Lewisham
- Kingsland in Hackney
- Knightsbridge in Kensington and Chelsea
- Silvertown in Newham
- Woolwich in Greenwich
A London Fire Brigade spokesman said of the Apollo collapse:
"If the same incident were to happen after the closures we would still have the resources to attend in good time and meet attendance targets."
Three of the eight fire stations that sent engines to the Apollo Theatre last night following the ceiling collapse that injured more than 70 people are set to close under the mayor's plans.
Westminster, Knightsbridge and Southwark stations are all earmarked for closure on January 9 2014
The application for judicial review was brought by the borough councils of Islington, Camden, Southwark, Tower Hamlets,Hackney, Lewisham and Greenwich.
The Fire Brigades Union has fought the proposed closures, which are part of a drive to save £28.8 million and have led to demonstrations across London.
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."
Eight London town halls today made a last-minute plea to Local Government Secretary Eric Pickles to stop sweeping fire service cuts.
Boris Johnson ruled earlier this month that his plan to axe 10 fire stations, 14 fire engines and 552 firefighters in the capital would go ahead.
But the local authorities, all Labour-run, have written to the Cabinet minister who has ultimate responsibility for the fire and rescue service, asking him to overrule the Mayor's decision.
Camden, Greenwich, Hackney, Islington, Lewisham, Southwark, Tower Hamlets and Waltham Forest argue the closure plan will disproportionately affect public safety in their boroughs.
They claim it ignores the fire risks posed by potential terrorist targets and a concentration of tourist attractions, as well as social and student housing, and the challenges of fighting fires in high-rise buildings.
Mr Johnson insists that the cuts - part of plans to save £28.8 million - will not impact on public safety, and that fire deaths in the capital are falling.