Nottingham high school for boys and Dayncourt comprehensive are well respected in their communities, relative high-performers and less than four miles apart.

But that is where the similarities end. The high school, founded in 1513, is the very picture of private-school elegance. Set in magnificent buildings just outside Nottingham city centre, it boasts arguably the best educational facilities in the county and has an average of 10 children to a class.

Dayncourt is quite different. Other than the odd lick of paint, there has been no real building work since the early 1970s. Some of the changing-room showers were condemned last year, class sizes are more than double that at the high school and five teachers will be laid off at the end of this year to save money.

But then you don’t have to look to hard to find the reasons for the huge divide... a split which strikes at the heart of Gordon Brown’s attempts to close the funding gap between private and state schools.

Last week the Chancellor, in his Budget statement, said that spending on maintained-school buildings would rise to private-sector levels by 2011, and vowed that class sizes would soon be similar on both sizes of the educational divide (see panel below).

But an analysis of Nottingham high and Dayncourt proves how hard it will be to turn his rhetoric into educational reality. Nottingham high is certainly not one of the most elite private schools in the country, but enjoys more wealth than many.

Annual fees for senior pupils are pound;8,394, cash which, given the school’s lack of public-sector bureaucracy, goes almost 100 per cent into the children’s education. Facilities include a 25-metre swimming pool, a climbing wall, fitness suite and a 20-acre playing field with cricket pitches so lush that the Australian, New Zealand and Indian national sides have practised on them in recent years.

In 2005, the high school, which spends pound;350,000 of its own money to fund pupils from deprived backgrounds, and a further pound;97,000 on scholarships every year, opened a new pound;1.1m arts centre - a move which underlines its long history as a hub of the creative arts (former pupils include DH Lawrence and prize-winning author Robert McFarlane).

Its 842 pupils, who can take subjects such as classical civilisation, Greek, philosophy and politics at A-level, are often in classes of 10 or so. The low pupil:teacher ratio helped every GCSE candidate last year to gain at least five good grades, while almost 70 per cent of papers were awarded As or A*s.

In terms of resources, Dayncourt could not be further away. The school, on the southern edge of Nottingham, was built in the early 1950s and extended some 20 years later to accommodate children whose parents moved to the area after a coal mine opened.

Hardly any building work has been done since. This year, the school has 938 pupils and a budget of pound;3.9m, including some pound;122,000 gained courtesy of its specialist sports college status. This gave Phillip Clarke, the head, pound;4,150 to spend per pupil - almost half the amount enjoyed at Nottingham high, and lower than the pound;5,000 described by Mr Brown as the state-school average.

After a four-year application process, Dayncourt has been told it will get a pound;750,000 all-weather football pitch and new changing rooms, but these will not mask the decay elsewhere in the school.

In the past 12 months, some of the showers were condemned by the local council after failing a health and safety inspection. Other changing rooms, says Mr Clarke, are in a “dire” state and the sports hall, part of the 1970s block, is in “terrible condition”. It, too, has a pool, but it was funded by the local swimming club.

Dayncourt, which comes under Nottinghamshire council, one of the country’s worst-funded shire counties, will lose five teachers and pound;50,000-worth of support staff to make up a pound;189,000 deficit by September.

There are 25 to 29 pupils in the typical key stage 3 class, although numbers fall to around 12 in the sixth form. Nevertheless, the school does well on its relatively low budget. Last October, Ofsted described it as satisfactory with “good features”, and said that pupils “enjoy school life in a safe and secure environment, where they are encouraged to learn”.

Fifty-four per cent of pupils gain at least five A*-C grades at GCSE.

But Mr Brown has a long way to go if Dayncourt is to ever look upon Nottingham high with anything other than envious eyes.