Michael Gove has been warned of a major flaw in the practice of allowing academies to determine their own admission policies in a letter from the prime minister's local Tory-led county council.

Academies can turn pupils away even when they have surplus capacity, according to Oxfordshire county council. This forces councils to pay to transport children to other schools. It claims the policy potentially puts at risk the option for parents to send their children to a "good, local school" and wants such admission freedoms to be fettered.

In its letter, which has been seen by the Observer, the council says that while it supports the academies programme, it will not be uncritical of "aspects which might not work in the best interests of local families and their children".

The development came at the end of a week in which Labour proposed policies to pull back from what has been described as the "Balkanisation" of the education system. A report by former Labour education secretary David Blunkett, published last week, proposed making academies and free schools accountable to regional commissioners appointed by local authorities.

In a sign of growing cross-party concern about Gove's reforms, Oxfordshire's letter, written by its Conservative cabinet member for education, Melinda Tilley, says: "The one which is currently exercising the council is the circumstance in which an academy publishes an admission number which does not accurately reflect its actual capacity, and refuses to admit additional local children despite there being demonstrable demand. In consequence, the council, at no little expense, may be obliged to transport as many as 30 children to a school in a neighbouring county or put them on a train to an inadequate school, a daily return journey of 30 or so miles. If the academy in question were a maintained school, the council would not hesitate (as the admissions authority for the school) to direct it to admit the additional pupils."

Under Gove's reforms, academies can implement their own admissions code. A small but growing number of schools, mainly sponsored academies, use ability banding as part of their criteria, according to research by the London School of Economics on behalf of the Sutton Trust. Schools might turn away pupils who do not fall into the right band, even when there are surplus places.

The Oxfordshire letter, which is also signed by Labour, the Liberal Democrats and the Greens, says: "The scenario described is theoretical, but was triggered by just such a sequence of events in relation to an Oxfordshire academy."

Oxfordshire proposes "some mechanism to fetter that freedom in the event that it is going to be exercised in such a way as to incur unnecessary additional costs". Its letter adds: "This might, for example, extend to the local authority the power to direct admission (as it currently has in relation to schools for which it is the admissions authority) but only in the circumstances describedabove."

Professor John Howson, the Liberal Democrat education spokesman on the council and a former government adviser, said Gove had "created freedoms without understanding the consequences".

A DfE spokesman said: "If an academy wishes to decrease their published admissions number, they must consult with their council, other local schools and parents beforehand. Councils have the power to request that places are offered if there are concerns that an academy is failing to comply with fair-access protocols."The council, which says the majority of its secondary schools are now academies, operating outside the supervision of local authorities, asks Gove or his officials to "give serious consideration to the issue and possible solutions to it".