It follows a shake-up of the complicated formula used to calculate how much cash individual schools receive from the government's central funding pot.
Previously local authorities were free to choose from a range of 37 factors when designing the formula that determines how much each school receives.
This allowed local councils some flexibility, ensuring allocated funds reflected local needs and priorities, including an "additional funding allowance" to protect small schools.
The new system is being introduced following government claims that inconsistencies and a lack of transparency meant a clearer, fairer and more consistent system was needed.
Councils are now required to consider 11 factors - such as deprivation, numbers of children and special educational needs - when designing their "funding forumula".
The government has moved to minimise any disruption by allowing councils to allocate a lump sum of between £0 and £200,000 to all schools under their jurisdiction.
But the flexibility to include an additional funding allowance has been removed.
This is expected to have a big impact in rural areas.
In Cumbria, for example, some schools would face significant financial challenges, said Cumbria County Council leader Eddie Martin.
The new arrangements significantly changed how the funding pot would be split between schools, he added.
Of the county's 310 schools, a best-case scenario would see budgets increase by up to 35% at 132 schools, with budgets decreasing by as much as 31% at 32 schools.
Changes at those 32 schools would affect 7,101 pupils. The remaining 146 schools would see little change.
Mr Martin said it was clear changes would not be limited to just those schools affected by budget cuts.
In such a large and diverse county, it was important that the right geographic spread of schools was maintained, he warned.
Over the next two years, the council would explore ways of ensuring schools were located where they were needed.
"This is a massive issue for Cumbria and I strongly believe that we need much longer than two years to implement these changes," said Mr Martin.
"Even with our best efforts to minimise the negative impact some schools would still lose out.
"I don't disagree that the old system needed updating, arguably it wasn't always fair how funding was allocated.
"But Cumbria is different to many other parts of the country and this new system risks major disruption for schools, pupils, staff and communities."
In some cases, itt would mean young children travelling very large distances to get an education.
"This is simply not acceptable and precisely why we have always previously made special allowance for these circumstances."
Local MP tim Farron said he feared the 32 schools facing the biggest budget cuts could be axed.
He has launched a campaign to keep small rural schools open.
"Small rural schools are the lifeblood of our community and they are vital to village life for many places across Cumbria. The thought of nearly 50 of them closing is something I cannot and will not accept."
Councils must notify the Department for Education of their new funding arrangements by 31 October.