Fifteen per cent of his pupils at Quarrendon upper school in Aylesbury, Buckinghamshire, got five Cs or better in GCSEs including English and maths last year, although the school is aiming to increase that to 32 per cent this year.
A third of the secondary modern's 775 pupils have special needs.
Mr Johnson said: "People think Buckinghamshire is all leafy suburbs but there are areas of deprivation and we are slap bang in the middle of them.
Pupils have low aspirations which we have to meet head-on."
Mr Johnson, who took over as headteacher in January, said that official statistics paid too little attention to vocational qualifications which engage pupils who would otherwise be at risk of truancy.
He said: "It comes down to schools providing experiences that match pupils' interests. I think it would be wrong to say schools cannot get specialist status based only on their GCSE results.
"Some schools may well perform really well on value-added measures but still get below 25 per cent A*-C grades including English and maths."
Mr Johnson said that the pursuit of specialist status could undermine schools' efforts to meet the needs of all children by encouraging them to focus on one curriculum area to the detriment of others.
"That causes us problems. I firmly believe if there was a specialist status in personalised learning this school would get it."
Mr Johnson backed Sir Cyril's call for more partnerships between high and low performing schools. But he believes it is "too early to say" whether using the Government's new trust status will help or hinder efforts to improve schools like his.
Quarrendon, currently in special measures, is part of a leading-edge partnership with two local secondaries which includes curriculum development activities on Shakespeare and jazz music and joint training for teachers.