The Public Accounts Committee also recommended that academies should collaborate with neighbouring schools and called for ministers to reject any new academy plans that threaten the viability of existing state education.
The committee wants academies to report annually on their admissions and exclusions to give parents and local communities "continuous evidence" that the state-funded independent schools are acting fairly.
It also noted that of the first 26 academy buildings, 17 had cost overruns averaging pound;3.2 million - well above 10 per cent.
In 2004, The TES revealed that two academies - King's Academy in Middlesborough and West London Academy in Ealing - had paid out large sums of money to companies in which their respective sponsors - Sir Peter Vardy, the Christian fundamentalist car dealer, and Alec Reed, the recruitment tycoon - had major interests, for services not put out to competitive tender.
And last month The TES uncovered another deal involving a Vardy-sponsored academy: a pound;20 million contract was given, without competitive tender, to a company run by David Vardy, Sir Peter's brother, who picked up a pound;71,942 salary package as part of the deal.
In both cases, the Government told The TES it was happy with the arrangements. But in evidence to the PAC, Peter Houten, academies director for the then Department for Education and Skills, gave a different impression.
He told the committee that academies awarding contracts to sponsors without going through the normal tendering process would be breaking public procurement law.
In response, the committee said: "A small number of academies have paid sponsors to provide services. Such services should be routinely put out to competitive tender so that they meet existing procurement regulations and demonstrably avoid conflicts of interest."
Academies have been criticised for isolationism. The committee called for a change because their sixth forms are small and have standards below national averages - a point also picked up by this week's chief inspector's annual report.
The Ofsted report says that collaboration with neighbouring schools, colleges, other training providers and employers would give academy pupils the best range of post-16 options and help to improve standards.
The MPs called on ministers to reject academy proposals that "put at risk the viability of local schools and colleges providing a good quality education, including proposals relating to education from age 16".
They warned that as more costly academies open there is an increasing risk that they will not represent value for money.
The report said that while existing academies have made progress in raising pupils' GCSE scores, it is too early to tell whether the improvement is sustainable.
Edward Leigh, PAC chairman, said it was too early to give an overall verdict on the success of academies, which so far present a mixed picture. His committee wants government to adopt a more systematic approach to learning lessons from the scheme.