Documents, obtained by The TES under the Freedom of Information Act, have reignited a row between the two senior education figures over the Office for Standards in Education inspection in 1997.
Professor Woodhead insists that he did not ask inspectors to alter any of their judgements.
However, the papers include a memo in which he demanded that extra information be added to the Birmingham report about Professor Brighouse.
"Given the chief education officer's huge personal impact, we need, I think, a section on his style, leadership, etc," he said. "I say this because he deserves to receive the public recognition and because I worry about the transferability of the Birmingham approach - does it depend too much upon one very unusual man?"
Education officials in Birmingham had been concerned before the inspection that Ofsted's judgements might be biased because of animosity between Professor Woodhead and Professor Brighouse, who were both on the Government's standards taskforce.
Professor Brighouse had been highly critical of the inspectorate, while Professor Woodhead was sceptical about the education director's liberal approach.
Professor Woodhead rejected a request by Professor Brighouse that he should have no involvement in the Birmingham report but promised he would only provide a "quality assurance function".
David Singleton, then head of Ofsted's local authority division, told Professor Brighouse in October 1997 that the chief inspector had no thought of altering the judgements.
However, the following month Professor Woodhead sent Mr Singleton a private memo demanding extra financial information about Birmingham so he could check the figures with a private accountancy firm. A subsequent letter outlined serious concerns about the Birmingham report, including that many sections seemed "little more than a tissue of assertion".
Professor Brighouse, now London schools commissioner, said: "I never doubted that Woodhead was interfering in the report.He went far beyond quality control."
Professor Woodhead, now chairman of the private schools firm Cognita, said:
"If you are suggesting I was trying to change the substance of the report I would dispute that view strongly.
"The memo told the inspectors to work on the story they were already telling, but to explore it with maximum clarity."