Labour MP Meg Hillier, who chairs the Public Accounts Committee, said the Education Funding Agency, which oversees free schools, had paid above the market value in 60% of cases.
And some purchased sites had later been deemed unsuitable to turn into schools.
The government said it paid over the odds only if there was no alternative.
Ms Hillier said in her constituency of Hackney South and Shoreditch civil servants had purchased the former police station for £7.6m - even though it had been valued at £3m six months previously.
The site was bought as a potential permanent home for the Olive School - an Islamic faith school - currently housed in temporary accommodation nearby.
But, after the sale had gone through, Hackney Council refused planning permission to convert the property to a school.
An appeal against that decision will be considered in a six-day hearing in June.
Ms Hillier said: "There is a real concern about whether the Olive School will ever open.
"Children are being taught at a temporary site - it is not good for pupils, and it is not good for the taxpayer."
But a Department for Education (DfE) representative said: "Hackney Police Station represented the best value option to meet the school's needs at the time of purchase.
"The site had been marketed openly, and the competition for it was such that the vendor received offers in excess of the original valuation.
"In this context, we believe we secured this site for the best price possible."
But Ms Hillier said many MPs and councillors in England could "name sites in their areas that have been bought for more than their market value".
"The Education Funding Agency is one of the biggest purchasers of land in the country - and it keeps paying over the odds," she said.
"People see the EFA coming.
"The desire to build 500 new free schools by 2020 means there is a rush to secure sites."
Ms Hillier added: "It is a real worry and not getting value for money for the taxpayer."
In response, the DfE said it would be launching a government owned company called LocatEd that would be led by property experts and responsible for securing sites quickly and providing good value for the taxpayer.
"We do not pay in excess of what a site is worth or purchase expensive sites if there are better value for money alternatives in the area," a representative said.
"The construction costs of a newly built free school are 29% lower than schools built under the previous school building programme."
The representative added: "Free schools are playing a vital role in creating more good school places.
"They are popular with parents, ensuring thousands more families have the choice of a good local school."
Too much money is being paid for the land and buildings needed for new government-funded free schools, the Commons spending watchdog has said.