Schools and other vital services in Leeds will be hit by cuts in government funding, according to the city council.
The forecast comes after the government announced more than £1.6bn would be axed from local authorities, with Leeds losing more than £7m.
Leeds council leader Keith Wakefield said the cuts would impact all services, including schools and support for families in deprived areas.
Bradford council is also facing a budget reduction of more than £7.26m.
Mr Wakefield said: "Over £5m has been cut from grants which the previous government provided to support services which are vital to young people who would otherwise not access education, employment or training.
"These cuts will hit our schools and undermine support for families in some of our most deprived areas."
He added: "We are still looking at the detail but it is apparent the cuts will have implications across all services, affect young people and impact on our work with the voluntary sector."
In March, the authority revealed plans to reduce spending in anticipation of government cuts.
As a result of that, the council said more than 1,400 jobs would be axed in the next three to five years.
In Bradford, plans to give free meals to primary school pupils in the city have been scrapped under the government spending cuts.
The authority has been told by the Department for Education that the year-long £8.34m pilot, which was due to start in September, has been withdrawn.
The council said it was assessing details of the other government cuts but it aimed to protect front-line services.
Becky Hellard, strategic director of corporate affairs, said: "Savings have already been identified, with the aim of protecting front-line services, and this work will continue.
"The council is looking to manage any reductions in employees as far as possible through turnover of staff and controlling vacancies."