A series of emails showed that civil servants repeatedly recommended that primary results should not be released on the same day as GCSE scores.
The messages, released by the Statistics Commission, an independent watchdog, revealed how officials wanted to publish results for seven and 11-year-olds two days before the GCSEs, which soared to a record high this year.
But they were overturned by Mr Johnson's advisers, who said they "positively want(ed)" the two sets of data to be released on the same day.
The Department for Education and Skills said the results, which showed falling standards in reading, writing and arithmetic at key stage 1 and missed targets for pupils aged 11, were published as early as possible.
Yesterday the commission was expected to make a series of recommendations to ministers, reforming the way exam results are released in the future.
The watchdog was expected to recommend that education officials be stripped of their powers to set dates for the publication of test results, releasing all future statistics on a fixed date. They may also request more information relating to the decision to release primary school and GCSE data on the same day.
But critics called for an explanation. David Willetts, the shadow education secretary, said: "It is wrong for political advisers to make decisions which reduce the public scrutiny of exam results. This has the whiff of previous scandals about 'burying bad news'."
Primary figures were published at the same time as GCSE results - 9.30am on Thursday, August 24. It marked a change from previous years when they were released on separate days.
According to the emails, Tracey Beames, of the strategic communications planning unit, and Ruma Multani, a DfES press officer, raised concerns on July 12 about the plans to publish KS12 and GCSE results on the same day.
But Andrew McCully, DfES director of school standards, wrote back: "We positively want it to be 24th."
The code of practice on government statistics states that figures should be released as soon as they are available and at a time that promotes "widespread access and informed debate".
A DfES spokesman said: "The department's chief statistician has confirmed to the Statistics Commission that the correct procedures were followed. "
Mr Johnson faced further criticism on Monday from Jamie Oliver on his new TV show, Jamie's Return to School Dinners.
The chef rebuked Mr Johnson after the Education Secretary said schools could not impose a ban on junk food because "there is an issue of personal liberty".