Ministers included science results in the latest set of tables measuring the performance of secondary schools in England at GCSE.

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But schools were marked down if pupils studied only two out of the three sciences under the new rules, even if the courses were more difficult.

State school pupils have to study elements of biology, chemistry and physics – often in combined "double science" courses worth two GCSEs, or a smaller combined science course worth one GCSE.

But many independent schools encourage pupils to take three separate GCSEs in the sciences, requiring more detailed study.

Under the Government's rules, the results of private school pupils who take two separate science GCSEs – for example in chemistry and physics, but not biology – are not valid for inclusion in the league tables.

According to the Government, all three sciences must be studied in some way for results to count in the rankings.

The Independent Schools Council (ISC) reacted angrily as dozens of private schools appeared near the bottom of the tables for science results.

Chief executive Jonathan Shephard said: "These flawed and misleading tables are a travesty of fair reporting.

"Children who gain two A* grades in separate science subjects are ranked below children who gain a single grade C in combined science."

He also condemned the exclusion of private school results for International GCSEs, which are seen as harder.

"Children who take the demanding International GCSE examinations are given no credit at all," Mr Shephard said.

"It is time for common sense to prevail and for these silly tables to be scrapped."

Pocklington School's results were affected because the majority of its students sat an international maths exam not recognised by the Government. The school's director of studies Rob Smith said: "If International GCSE results were included, the table would show that 96.4 per cent of the cohort who sat GCSE examinations at Pocklington in the summer of 2007 achieved five or more A* to C grades including mathematics and English."