Locals, firefighters and other emergency services workers picked through the rubble to find those trapped, in chaotic scenes.
"We worked through the night and one body was recovered", the southwest coordinator of the National Emergency Management Agency (NEMA), Ibrahim Farinloye, told AFP. "The debris has been cleared", Adebayo said. Final casualty figures were still being compiled and would be announced later, he said.
"So far, from what I have been briefed, we have rescued about 25 people and some are already dead but we were earlier informed that it was a school, the building is not technically a school, it is a residential building that was actually accommodating an illegal school so to speak on the second floor".
Lagos Governor Akinwuni Ambode, who visited the site hours after the building collapsed, said the school had been set up illegally and that buildings in the area had been undergoing structural testing prior to the accident.
"We cleared it out to see if anyone was still buried below this rubble", he said.
Shopworker Adeniyi Afolabi, who lives nearby, gave the name of the school as the Ohen Nursery and Primary, and said there were 144 pupils in attendance on Wednesday. Both said not all children were at the school because of sports activities.
Lagos, which has a population of 20 million people, is made up of a collection of islands.
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Building collapses are tragically common in Lagos and elsewhere in Nigeria, because of the use of sub-standard materials and the non-enforcement of building regulations.
In September 2014, 116 people died - 84 of them South Africans - when a six-storey building collapsed in Lagos where a celebrity televangelist was preaching.
Dr Hussaini Abdu, Country Director of Plan International Nigeria, called on the Lagos state government to launch an inquiry into the incident. Engineers responsible for the construction are now on trial for manslaughter.
Two manslaughter prosecutions are now being held in Lagos state after scores of people were killed in two separate building collapses in 2015 and 2016.
It is not yet known what caused the collapse of the building, which had been earmarked for demolition.
"These houses are not safe".
Despite efforts to renovate the area, a large number of abandoned buildings have been taken over by families or businesses, despite being dilapidated and unsafe. "We are about to enter the rainy season and these things will get worse", she added.