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.
More top news
Chelsea won the first domestic trophy of the season thanks to a 2-0 win over London rivals Spurs at Wembley.
An online video showing a naked man apparently falling down the outside of Buckingham Palace has split opinion online - is it a hoax?
A new market has started up in London championing the production of sustainably produced, local food.