The Tottenham mop-top remains its most illustrious former pupil, despite an anticlimactic World Youth Cup in Australia. His stunning goals and wholesome image have helped to counter the negative publicity which the School, nestling in rural Shropshire at the National Sports Centre at Lilleshall, has endured since the first batch of England's best 14-year-old players arrived in 1984.
Where, the critics have demanded, is the international elite which Bobby Robson, national manager at the time of its inception, envisaged its producing? And couldn't the resources - which come exclusively from FA coffers since sponsorship ended in 1991 - be better used elsewhere?
The first question could be answered before long by the 19-year-old striker from Humberside; the second when the FA reviews the School's future on its 10th anniversary in 1994. But according to Keith Blunt, the former teacher and Spurs youth coach who is now in his second year as its technical director, perceptions are becoming more positive.
'Barmby has undoubtedly been the catalyst,' he says. 'Because of him, people who perhaps sneered at this place without bothering to find out what we're about are saying, 'Perhaps there's something in it after all.' '
Blunt reels off an impressive list of Lilleshall alumni. Garry Flitcroft, who might even beat Barmby to international honours, did his two years there; as did Mark Robins and Bryan Small, now vying to become the first graduate to win a championship medal; Andrew Cole, Newcastle's pounds 1.75m recruit; plus John Ebbrell, Graham Stuart and Ian Walker.
Hard on their heels are Andy Turner, Mark Flatts and Andrew Myers, who have already sampled the Premier League with Spurs, Arsenal and Chelsea respectively, and Jamie Forrester, who made his Leeds debut at Nottingham Forest on Sunday.
This roll-call does not impress Malcolm Berry, chief executive of the English Schools' Football Association and an FA Council member, who is one of the School's more constructive critics. 'They didn't 'produce' Barmby,' he says. 'We did, through the work of teachers and coaches before he went there. He was already outstanding. They simply finished him off.'
Berry argues that the money spent on the School - which he puts at pounds 500,000 a year though the FA do not publish figures - ought to be invested in the 150 regional 'centres of excellence', most of which are attached to professional clubs. 'That way, the better boys could have regular residential courses, and many more would receive proper instruction.
'We don't believe you have to take a boy away from home and hide him away in the country to give him a football education. It's fine if he's living in the Midlands, but to uproot him from Newcastle or Plymouth seems quite unnecessary.
'You can't pick out budding Bryan Robsons at 14 anyway, but it's also a question of numbers. The selection policy, whereby they can take only 16 boys a year, is too narrow and elitist.'
Blunt recognises 'some merit' in the charge, and is revising the selection procedure accordingly, but dismisses the idea of diverting cash into local centres. 'That's absolute nonsense. I've worked in those places, and you can't compare their quality of work with the influence of a residential education. You only have the boys for an hour . . . the rest of the time they're playing for everyone.'
Here, at least, he and his friend, Berry, are in agreement: boys play far too much competitive, 11-a-side football, frequently causing stress fractures that can end a career before it has begun.
Berry talks about the need to 'stop exploiting talent rather than developing it', and suggests the way to do it is by 'changing attitudes'. There he parts company with Blunt, who pointedly asserts the importance of removing gifted youngsters from 'the rat race and the idiotic demands placed on them by some of our critics'.
He maintains that the ESFA, under whose aegis an England Under-15 side including six Lilleshall boys lost 2-1 to Scotland at Wembley this month, tend to pick out bigger youths because of the need to win matches. The School would not ignore a strapping six-footer - he might be the new John Charles or Duncan Edwards - but it now casts the net wider.
Some boys of 14 are, he explains, built like 16-year-olds; others like 12- year-olds. 'As the smaller boys with quicker feet grow, they leave the big ones behind. It happened with David Platt, who was tiny until late adolescence, and Adrian Littlejohn is another example. Initially he didn't do very well on leaving here, but has now developed physiologically and is a regular with Sheffield United.
'We're looking for football intelligence, boys who read the game well and have the right instincts. What we can help with is technique and temperament. If we can ally those aspects to the strengths we already have in this country - organisation, aerial power, tenacity - we'll be doing a valuable job.'
The School is reputedly nicknamed 'The Prison', but former pupils who will criticise it publicly are scarce. Alan Miller, understudy to David Seaman at Arsenal, reckons it gave him 'a great start' by preparing him for life at a club. (Miller also gained five O-levels at the comprehensive all pupils attend - 'probably better than I'd have done at home'.)
Alex Ferguson, whose Manchester United youth team includes Richard Irving from the class of '92, calls attacks on Lilleshall 'nitpicking', adding: 'You have to examine it in the context of the percentage of young players who come through at a club.'
Berry, too, acknowledges that the experience benefits some. 'John Ebbrell, of Everton, was at a rugby- playing school, so it helped him develop his skills. And it's clearly good for those boys whose home backgrounds are rather poor.'
But for the ESFA, the Barmbys and Flitcrofts do not alter the fact that the School is a drain on resources. 'Here we are with 15,000 schools in membership, having to flog ourselves silly to raise money to keep the sport going,' Berry says. 'For the good of the game - at all levels - we need a properly funded excellence scheme. We don't need the FA School.'
He observes wryly that the goalposts have been moved over the past decade. 'The School now say: 'Ah, but we're not specifically looking for boys able to play international football - we're looking to the future'.'
Blunt, currently defying gloomy forecasts of the School's demise by staging trials and interviews for next year's places, would not argue with that. 'In football, everyone wants instant results,' he says. 'But if you start a project of this magnitude you don't get it right straight away.
'I'm very excited about some of the prospects here. If five or six a year go on to the Premier League, we'll have been successful. And if we could get one international from each intake, that would be a great achievement. While the School isn't the complete answer some people envisaged, it's certainly worth persevering with.'
SCHOOL FACT FILE
First graduate to make League debut: Ian Chapman (Brighton).
First to command transfer fee: Andrew Marriott (Arsenal to Nottingham Forest, pounds 50,000).
First to command six/seven-figure fee: Andrew Cole (Arsenal to Bristol City pounds 500,000; Bristol City to Newcastle pounds 1.75m).
First to win Under-21 cap: John Ebbrell (Everton).
Youngest Premier League (then First Division) debut: Andrew Myers (Chelsea), 17yrs 5mths.
More than 40 per cent of graduates have made their senior debuts.
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