As many as one in four pupils could have their test scores reviewed because of the fiasco engulfing the exam system, head teachers have warned.

A mass remark on this scale – potentially involving the papers of 300,000 children – would plunge the exam system into new chaos and call into question the competence of Ed Balls, the schools secretary.

Pressure is mounting on Ken Boston, chief executive of the Qualifications and Curriculum Authority (QCA), which gave the doomed £156m deal to ETS, the firm which has bungled.

Once this year’s marking has been sorted out, relations with ETS are expected to be severed following talks which began last Friday afternoon.

Boston’s legal team are now haggling with the firm. ETS will try to minimise any recompense it has to pay for its errors while the QCA will try to ensure minimal – if any – compensation is payable should ETS’s severance terms be invoked. “Balls, the QCA, ETS, they all want out,” said one political source.

The removal of ETS will not bring an early end to this year’s delays and mistakes and further uncertainty looms while a new testing company is chosen.

Michael Gove, the shadow schools secretary, blamed Balls for overloading the QCA with initiatives and reforms. “All of this has been driven by Ed Balls,” he said.

The prospect of mass appeals over the Standard Assessment Tests (Sats) for 1.2m 11-and 14-year-olds has grown as concern switches from scripts delayed and lost to the accuracy of the marking itself. Mick Brookes, general secretary of the National Association of Head Teachers, described the problems as “unprecedented”.

He said he was so worried about the reliability of the scores that he was advising schools to submit papers for appeal if they had even the slightest concern. “We estimate there could be appeals on up to 25% of papers,” said Brookes.

This weekend evidence of poor-quality marking continued to mount. “Right from the beginning it’s been a fiasco,” said Ron Naylor, head teacher of Forefield junior school in Crosby, Liverpool. “The standard of marking on the English papers that we have now got back is absolutely appalling.

“The kids who are excellent writers got worse marks than the terrible writers. We’re going to appeal, although it’s a lengthy process.”

ETS said this weekend 800 schools had already launched appeals. Test results for 29% of English papers for 14-year-olds were still not available and an estimated 120,000 children are likely to go into their summer holidays without knowing their full test results.

For many, it may mean disruption to the beginning of their secondary school careers as teachers use Sats results for 11-year-olds to allocate them to suitable classes.

ETS had been due to release results to schools by July 8 and the shambles has been blamed on a lack of trained markers, understaffed helplines and inadequate computer systems.

Boston and the QCA have been accused of failures including lack of contingency planning, failure to learn from major mistakes in 2004 and inadequate vetting of ETS.

In March this year, Boston told Balls he would cope with any problems from the new contract, saying: “We are aware that the introduction of new IT-based improvements must carry risks, but we have mitigation plans to ensure delivery is secure.”

The Tories, who are expected to announce reform proposals for the testing system this week, believe Balls cannot escape responsibility.

“Of course there is huge responsibility on Ken Boston, who is one of the best-rewarded public servants in Britain,” said Gove. “But ministers must be held accountable for the huge load they have put on this creaking structure.

“Not only are the QCA responsible for running tests with this new supplier, but they are being restructured, are overhauling the curriculum for 11-to 14-year-olds and GCSEs, delivering the government’s new diplomas and moving headquarters.” Final responsibility for these initiatives rests with Balls, he said.

Boston and Kathleen Tattersall, who chairs Ofqual, the new exams regulator, began last week maintaining the problem was “logistics”. By the end of the week, the issue was becoming the accuracy of the marking. Tattersall said that if serious problems over quality were identified, she could refer the tests to Balls to consider scrapping them.

Strong anecdotal evidence over accuracy is already starting to emerge. James Elliott, head teacher at Talbot combined school in Poole, Dorset, said: “When some of our papers did finally arrive last week, the maths papers had been returned totally unmarked. Secondary schools use these tests as the basis of their class groupings. It’s very hard on the kids to be left in limbo like this.”

Other evidence has included marks added up wrongly and “totally implausible” differences in reading and writing scores given to the same pupil.

Lord Sutherland, the former chief schools inspector appointed to inquire into the debacle, is not due to report until autumn.

The chaos is expected to be used by Brookes’s union and by the Association of School and College Leaders and the National Union of Teachers to press for sweeping test reforms.

ETS, based in Princeton, New Jersey, won its deal in February last year in a bidding process codenamed the “Tornado Project”. The QCA board congratulated Boston on the deal, with the chairman, the businessman Sir Anthony Greener, suggesting it should be a “case study” in “best practice”.

The deal with ETS, understood to have been £9m cheaper than other bids, may come back to haunt the board.

It has also been claimed the selection by the QCA and its advisers failed to take account of the firm’s record of problems in America. This included errors in tests for 4,000 trainee teachers resulting in payment of £5.5m compensation in 2006.

“This company has a history of overstretching itself to win contracts,” said Robert Schaeffer, public education director at FairTest, an exam monitoring group in Cambridge, Massachusetts. “This results in them not being able to deliver tests with the right quality or timeliness and the result has been failures and lost contracts.” ETS said the reason its mistakes were heavily attacked was that “the difference between ETS and others is that we say straight away when there are problems”.

Barry Sheerman, chairman of the schools select committee, said: “Here came this firm from America trying to set up an operation from scratch. That is why they ran into so much trouble. No wonder the QCA have been so wrong-footed.”

Additional reporting: Chris Gourlay and Bradley Green

Top marks: £300,000 a year and a Chelsea flat

The quangocrat at the centre of the testing fiasco is one of Britain’s highest-paid civil servants, writes Robert Watts.

Ken Boston, lured from Australia six years ago to sort out an earlier exam debacle, receives £328,000 in salary and perks. The package, greater than that paid to Mervyn King, governor of the Bank of England, jumped 15% from 2006-7 to 2007-8.

The remuneration for the 65-year-old chief executive of the Qualifications and Curriculum Authority (QCA) includes a flat in Chelsea, west London, and six business-class flights a year back home.

These can be used by Boston, his wife Yvonne or daughter Nathalie. Return flights to Sydney with British Airways typically cost £3,700 to £7,700.

UK tax rules allow foreign nationals working in the UK to receive travel costs tax-free for just five years. In an unusual arrangement, the QCA has met the cost of his tax on these benefits.

Boston, a member of the Royal Sydney Yacht Squadron, rose through the ranks of Australia’s educational bureaucracy.

After coming to Britain, he spent a spell in Knightsbridge before his move to Cathcart Road, Chelsea. The actor Hugh Grant is a neighbour. The rent on the flat is understood to represent the bulk of the £153,900 “benefits in kind” Boston received in 2007-8.

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