It comes despite a government pledge to add a "sparsity factor" to its funding formula that takes into account a school's location and pupil numbers.
Officials have suggested that rural schools will gain on average 1.3% in funding under the new funding formula.
But an analysis by the Times Educational Supplement based on the government's own figures suggests that 40% small schools will suffer a cut to their budgets.
It suggests that the schools could lose up to 1.2% in the first year of the new funding system, rising rise up to 2.5% in further years without transitional funding in place.
Nancy Lees, head of Castleton CofE Primary in Derbyshire, told the TES: "For us, it's really quite disastrous, because we are very, very small," she said.
"We have got 18 children on the roll. If we can't recoup money from somewhere, we will have to question the future viability of the school."
The F40 group, which campaigns for fair funding for schools, said before Christmas it needed time to analyse the detail within the government's announcement.
F40 chairman Ivan Ould said the group wanted time carefully assess the full implications, including the issue of local flexibility and details about the transitional arrangements.
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