The think tank said the city's 1,536 schools needed to save £360m in the first year if the government's National Funding Formula (NFF) plan goes ahead.
The amount is the equivalent of 12,857 qualified teachers, on an average salary of £28,000.
The government said London was the highest funded part of the country.
It added that under the plans, which are under consultation, inner-city schools would be allocated 30% more money per pupil than the national average.
But London Councils, which represents the city's 32 boroughs and the City, said no school would gain enough funding from the NFF to compensate for increased cost pressures from inflation, higher pension contributions and national insurance.
Ministers said the new formula was needed to tackle uneven levels of funding across England, with the best funded areas getting more than £6,300 per pupil per year, while the worst-funded averaging £4,200.
It said the funding cut was on top of National Audit Office figures which showed England schools faced an eight per cent real-terms cut per pupil by 2019-20 because it  wider cost pressures.
In a statement, London Councils said: "At a time when UK schools are seen as underperforming by international standards, and when businesses based in London are facing massive uncertainty about recruiting skilled staff, there is an urgent need to invest in schools in London and across the rest of the country."
It added: "Without the right qualifications and skills, London's children will be unable to access jobs and contribute to the national economy. Over 60% of jobs in inner London require a degree and around 45% of jobs in the rest of the capital require a degree."

The attacker, who was caught assaulting the woman in Holloway, north London, was jailed for six years by Blackfriars Crown Court.
The case went ahead under the assumed name Aurilien Cheyroux, as the authorities could not confirm his true identity, other than him being French.
The judge ruled he should be deported once his sentence was served.
Passers-by saw "Cheyroux" partially-dressed and struggling with a woman on Caledonian Road in the early hours of 1 March, the court heard.
He ran off, but was caught by witnesses and held until police arrived.
The woman told the witnesses she was uninjured and left the scene before police arrived.
The attacker told police he was a French national and gave the name used in the trial.
But after taking finger prints the French authorities said the information was incorrect. They were unable to establish a true identity.
Det Const Kip Malek said: "This is a highly unusual case where we have been unable to trace the victim and the man who has been convicted is under an assumed name.
"Despite this we have been able to get a conviction and that is due to the brave members of the public who witnessed the attack and took it upon themselves to pursue this man and contact us."
Cheyroux was found guilty of attempted rape but had previously pleading guilty to sexual assault.
Det Insp Neil Smithson added: "I am still keen to ascertain his identity. Equally, if you were the victim of this offence please contact us."

The home affairs minister said he was refused a visa as the constitution prohibits hate speech.
Mr Anderson runs the Faithful Word Baptist Church, which says that homosexuality is an abomination punishable by the death penalty.
He said that religious freedom no longer existed in South Africa.
"I feel sorry for people who live in South Africa, but thank God we still have a wide open door in Botswana," Mr Anderson posted on his Facebook page after the decision to refuse him a visa.
South Africa has one of the most liberal constitutions in the world which protects gay rights.
The BBC's Milton Nkosi in Johannesburg says Mr Anderson was invited by a local church to visit this month.
Two petitions with more than 60,000 signatures, organised by gay and human rights activists in South Africa, had called for the trip to be stopped.
"I have identified Steven Anderson as an undesirable person to travel to South Africa," Home Affairs Minister Malusi Gigaba said.
Mr Anderson's church is based in the US state of Arizona and describes itself as an "old-fashioned, independent, fundamental, King James Bible only, soul-winning Baptist church".
In a video posted on YouTube before South Africa's decision was made, he said that the trip was not going to be about homosexuality, but he stood by his views against homosexuality, which he said were endorsed by the Bible.
About 70% of London schools could face budget cuts under government plans to change how they are funded, according to London Councils.
[NEXT_CONCEPT]
A man has been jailed for attempted rape despite police not knowing who he is or finding his victim.
[NEXT_CONCEPT]
South Africa has barred controversial US pastor Steven Anderson from visiting the county because of his critical remarks about homosexuality.