Mr Humphrey accused the council of "smoke and mirrors", over a forecast deficit of £1m at the school over three years.
"There's no way they can rehome all of the children in this school, 40 or more of them with special educational needs, for less than a million pounds in the next three years," he said.
Helen Hayden, Leeds City Council's executive member for children and families, said closing a school was "not a decision we take lightly".
She said the council understood the strength of feeling, and recognised the "tireless work of everyone involved" in improving the school's position.
"As a local authority, we have a responsibility to consider the viability of the school and as such, we are now seeking to progress to the next stage of consultation," she said.
"There will now be further opportunity for people to show their support or objection to the proposal during the new statutory notice period."
Hayden emphasised that the authority would "work closely with all affected families" and provide "comprehensive and bespoke support" for children with additional needs or EHCPs, "to ensure their needs continued to be met."
A final decision will be taken at the council's June executive board, and if approved, the school will close at the end of the summer term.