The National Foundation for Educational Research study found officials had less scope to use their discretion when allocating money because the Government has guaranteed all schools a minimum increase per pupil.
The report, to be presented to the Local Government Association's education conference, in Gateshead, next week, is the first phase of a wide-ranging study looking into the reforms.
It found that councils welcomed increased stability for schools as a result of three-year budgets to be introduced in 2006-7.
Overall, 101 of 148 local authorities responded, a return rate of 68 per cent.
Understanding of the new funding arrangements varied widely.
While 65 per cent of officials said they "completely" understood how the system worked, they believed that only 5 per cent of schools were as confident. Half of schools were said to understand the system "a little" and 44 per cent "quite a lot".
Almost half - 49 per cent - of respondents "strongly disagreed" or "disagreed" that the funding arrangements provided sufficient money for curriculum delivery.
Seven out 10 believed that the system offered more stability for schools.
However, 77 per cent said councils were now unable to cater for local needs, while 62 per cent said it fostered inequalities between schools.
Slightly more than 60 per cent said councils now had less control over budgets, and 56 per cent felt they were unable to use their discretion to help problem schools.
Alison King, chair of the LGA's children and young people board, said: "It is clear that the best option is to free up the current strait-jacket style funding regime and replace it with one which is controlled by locally elected, democratically accountable councils."