Local authorities which spent extra had been expecting to lose more than Pounds 250 million as a result of reforms to be introduced next year because of capped future funding increases.
As The TES reported earlier this month, schools in the predominantly rural areas affected were to get smaller increases in funding than those in urban areas where councils allocated less than expected to education.
The changes are part of a reform of the funding system which will significantly reduce the power of local authorities and is intended to ensure increases in education spending are passed on to schools.
School spending will be ring-fenced, preventing councils from diverting money to other services, and every school will be given a minimum guaranteed per-pupil increase.
The new dedicated school grant, as the ring-fenced money will be known, will increase by at least 6 per cent in 2006-7 and 2007-8.
Under the Government's original proposals, councils spending more than the Government recommends on education through higher council tax or reduced spending on other services would, in time, have had the extra redistributed among other councils. Those spending less on education in order to keep down local taxes or fund other priorities would have had their education spending increased at a faster rate.
Concerns raised in the consultation on the proposed arrangements have prompted ministers to rethink their plans and to promise a new consultation about the level of funding increases different councils can expect over the next few years.
In a written statement to parliament, Jacqui Smith, school standards minister, said one option under consideration was to give all councils a minimum increase of 5 per cent per pupil in 2006-7 and 2007-8.
Warwickshire, which led a campaign against the changes, had accused the Government of acting like "a reverse Robin Hood". Eric Wood, county education officer, said he was pleased the Government seemed to be listening: "This campaign was about ensuring we do not lose resources to authorities which already receive more money per pupil than we do."
Local authorities will be able to use money from their schools' budget to improve children's services as part of the Every Child Matters agenda, but only if it benefits schools and is approved by school forums which will be strengthened and given a greater role in decision making.
The level of the guarantee will be announced in the autumn. Schools with falling rolls will receive additional protection.
The Government has decided to press ahead with these changes despite criticism from the Audit Commission public spending watchdog and Commons education select committee which have criticised the per-pupil guarantee.
Ministers will review the guarantee for 2008-9.
Three-year budgets will be delayed until the same year with a two-year settlement for 2006-7 and 2007-8 to allow time to make administrative changes.
Ms Smith also confirmed the Government would continue with plans to merge most existing standards fund grants into a single school development grant.
John Dunford, general secretary of the Secondary Heads Association, said: "Schools need fewer funding streams and more funds in their core budgets. Today's announcement demonstrates that the Government is listening."