Many councils, including Birmingham, Telford & Wrekin, Wolverhampton and Staffordshire have pledged food or vouchers to help those most in need.
Today the Conservative leader of Walsall Council Mike Bird said it would cost the local authority £213,000 per week, which was money it did not have.
He also said it had a crisis fund to help families in need all year round.
Council defends not offering free school meals
BBC Radio WM
The leader of Walsall Council has defended the decision not to provide free meals in half term for vulnerable children, saying the local authority can't afford it.
The UK government extended free school meals to eligible children during the Easter holidays earlier this year and, after a high-profile campaign by footballer Marcus Rashford, did the same for the summer holiday.
But it has refused to do so again.
Some councils are providing meal vouchers, but Walsall council is not one of them.
Mike Bird, leader of the Conservative council said: "One of the main reasons being we haven’t got the money to
do it, if you do it for this half term, then the next request would be for
Christmas, Easter and the summer break and for Walsall council that means £1.5m and that's a figure we just haven't got.
He told BBC Radio WM the half term was a "foreseen expenditure".
"We're doing our bit," Mr Bird said, adding there was help available through the local authority's crisis fund.
"It’s no good feeding a child for just one week, it has
to be an all-round package, there has to be better ways of doing it than
throwing money at one week."