Cleaners at some Kirklees schools are being denied the Living Wage because of a loophole.
Last summer the council agreed to pay the higher rate, £8.25 per hour, to all its employees.
But cleaners and caretakers at 18 schools have been left out as they are employed by private firm SPIE.
The French company has the contract after it took over a Private Finance Initiative (PFI) deal from German firm Hochtief.
Members of Unison lobbied Kirklees Council’s Cabinet to call for action.
Paul Holmes, branch secretary of Kirklees Unison, said: “Our low paid members are incensed they have lost out by almost £1 an hour compared to Kirklees Council colleagues.
“If the council is serious about bringing in the Living Wage they will pressure a partner company to see sense.
“Unison is working hard to get the company to negotiate but they have now announced they don’t recognise the union.
“This is bully-boy tactics at its worst, but our members will not be pushed around.”
He told the Huddersfield Town Hall meeting that SPIE met legal requirements as it paid 37p above the minimum wage.
He added: “All companies should pay the Living Wage and recognise trade unions but there’s not a lot we can do as we haven’t the power over private companies.”