The letter emerged as heads of some of the most selective private schools branded the proposals as 'simplistic' as they attacked the Government of having had 'little positive impact on social mobility'.
Last week the Cabinet Office minister suggested firms ask a set of questions allowing them to check the 'socio economic background of those applying for jobs in an effort to stop discrimination against the poor.
But Chris Ramsey, head of King's School, where Mr Hancock was a pupil, wrote to the minister criticising his proposals.
In the letter, seen by the Daily Telegraph, Mr Ramsey said he was 'dismayed' by Mr Hancock's suggestions.
He wrote: "You must know, as an Old King’s Scholar, that having been educated at an independent school is not of itself an indicator of social advantage."
Separately, Mr Ramsey also said: "Well, I have more justification than some in taking issue with Matt Hancock, since he is an alumnus of the school whose Head I am. He’s an intelligent, charming and generous political rising star, but I think he has jumped on a bandwagon which has, to mix my metaphors, passed its sell-by date. He also said a student is not defined by their background.
He explained: "To give two obvious examples, why should a full-bursary student from a disadvantaged background, educated at, say, Christ’s Hospital School (an independent school with a noble tradition of social diversity), be categorised with a full fee-payer at, say, Eton? Or pitted against the ‘state educated’ middle-class pupil at, say, The Judd School or London Oratory, two schools with noble and impressive traditions of high academic performance and some very wealthy people in their parent body?"