Exam results have risen fastest in the most deprived areas since Labour came to power, a period during which they have received the lion’s share of extra funding.

The findings contradict claims by ministers’ critics that the pound;8 billion increase in annual expenditure on schools between 1998-2003 has been wasted.

A direct comparison between extra cash and improved exam results must be made with caution: the analysis highlights how the extra cash has been used to greater effect by different education authorities.

An extra pound spent in some local authorities results in standards rising up to 10 times faster than in others. Official figures on spending per pupil and GCSE results between 1997-2003 for each local authority in England were used to examine the impact of additional resources.

The proportion of pupils gaining five or more A*-C grade GCSEs in the 18 most disadvantaged authorities has increased by an average of 10.7 percentage points to 42.3 per cent since 1998, as spending rose by an average of pound;1,071 per pupil.

This compares with a 6.9 percentage point rise in the 15 most affluent areas which received a pound;593 increase. This year’s key-stage test results also showed traditionally low-performing authorities, where spending is higher, making big improvements.

Professor David Jesson, a league table expert at the University of York, said: “The signs to date certainly appear to confound those critics who suggest that additional funding never does equate to improved performance - while at the same time challenging all schools to show that they really are providing value-for-money in the performances they help their children achieve.”

Gaps between the impact of additional spending exist in both affluent and deprived areas, measured by the proportion of pupils eligible for free school meals.

Some of the differences are likely to be a result of local factors such as the size of the authority and the complexity of social problems in the area. But experts say that questions need to be asked of authorities who appear to provide poor value for money.

Improvement has cost most in North-east Lincolnshire, where schools have enjoyed an increase of pound;760 per pupil since 1998. The number of pupils gaining five or more A*-C grades in the authority has risen by just 1.9 points to 35.2 per cent, a cost of pound;400 per point.

By contrast, schools in Gateshead, an area with a similar level of deprivation, offer the second best value for money. Each percentage point improvement in GCSE scores in the north-east council cost only pound;44.

Rutland, which has only three secondary schools, performs best with pound;35 spent on each extra point.

If North-east Lincolnshire had managed to translate pounds into points at the national average rate for LEAs of 114.8 last year, 39.9 per cent of its pupils would have gained five good GCSEs.

Professor Alan Smithers, director of the centre for education and employment research at Buckingham university, said: “This is a very interesting study. It shows that extra spending has given a welcome boost to authorities such as Birmingham, Newham and Barking and Dagenham, with a high proportion of pupils eligible for free school meals.

“The interesting thing is what distinguishes these from authorities such as Greenwich and Blackburn with Darwen, where it does not seem to be paying off.”

A government spokesperson said: “We will continue to work with LEAs on our relentless drive to ensure that every pupil is given the opportunity they deserve to fulfil their potential.”