Russell Hobby, general secretary of the National Association of Head Teachers (NAHT), said the results were "excellent news".
"It shows the hard work that's going on in the system and has been going on for some years."
He said the majority of primaries will not be academies, which shows that schools can improve "no matter what their status".
More top news
More than one in five school staff have had a false allegation made against them by a pupil, according to a survey.
Parents of obese children rarely spot that their child is overweight, doctors warn.
MPs are no longer MPs, just candidates again - Parliament has automatically dissolved and the 'short campaign' begins today.