London's Fire Commissioner, Ron Dobson, had originally proposed closing 12 fire stations, reducing the number of fire engines by 18 and cutting 520 jobs.
A series of public meetings and other consultations were made, resulting in changes to the original plans, but they were still rejected by the fire authority.
In a letter to the authority's chairman, James Cleverly, the Mayor said action had to be taken so that savings could be made, otherwise the authority's spending for 2014/15 would be greater than its resources.
"This eventuality would not represent sound stewardship of public funds and would place both the Mayoralty and the authority in an unacceptable position," he said.
The Mayor warned that further delays to implementing the commissioner's proposals would increase the likelihood of compulsory redundancies.
"I am also mindful of the desirability - which I know LFEPA members share - of avoiding compulsory redundancies for firefighters. Further delays to the implementation of the Commissioner's proposals will increase the likelihood of compulsory redundancies."
Mr Dobson has stressed that safety standards would not be affected by his proposals, which have been opposed by the Fire Brigades Union.
A spokesman for the London Fire Brigade said: "The authority has now received and is considering the Mayor's direction."
The London Fire Commissioner Ron Dobson has said the Fire Brigade has improved its systems following the inquest into the Lakanal House fire. Six people died in the blaze in 2009.
One of the problems which was highlighted was that staff who answered 999 calls from residents did not have accurate information on the state of the fire. Nina Hossain spoke to Ron Dobson.
The 12-week consultation follows a row between London's Mayor Boris Johnson and members of the capital's fire authority, who have been opposed to the cost-cutting plans.
London Commissioner Ron Dobson insists existing response time targets will not be affected by the £45 million cuts. He said:
"Compared to 10 years ago, the brigade attends half as many fires, a third fewer house fires and almost a third fewer incidents overall. In the future, the resources available to the brigade will reduce and the number of people who can work for the brigade and provide our services will also reduce."
"We have passed the point where we can make the necessary level of savings without any impact on our fire stations."
Fire authority chairman James Cleverly (Conservative) said: "The plan outlines a range of proposals that together will ensure London Fire Brigade provides the public with the best fire and rescue service in the country while also playing its part in helping balance the nation's finances."
"Under these proposals more London boroughs will fall within the six-minute average attendance time target for the first fire engine to arrive at an emergency and the brigade's ability to deal with major incidents will be maintained."
The Fire Brigades Union and Labour, Liberal Democrat and Green party members of the fire authority are opposed to the station closures and job losses.