The recommendation was included in the new admissions code to help parents make better choices about their children's prospective school. It is designed to stop them wasting one of their preferences on grammar schools that already know which children have failed their admissions tests.
Schools and local authorities should have the system in place now as parents across the country choose school places for next September. However, many have failed to do so, claiming it would be difficult to organise setting, marking and returning the tests this early.
Kent Council which has 33 grammar schools, the highest number of any county, will hold a consultation on making the change but has not done so yet.
Other areas that still do not make 11-plus results available to parents before they choose schools include Buckinghamshire, Birmingham, Plymouth and Trafford.
Previously, pupils who failed the 11-plus could miss out on places at other popular schools if their local authority operated a preference system, and they ranked a grammar school first.
That system has been changed under the new code. But parents can still waste a choice on a grammar school if results of the 11-plus are not published early enough.
Other parents who knew their children had passed the 11-plus might want to put only grammar schools on their application form.
Brian Wills-Pope, chairman of the National Grammar Schools' Association, said parents should be told the results.
"That is the spirit of the law and if local authorities or schools drag their feet there will be complaints," he said.
Mark Tweedle, headteacher of Heckmondwike Grammar School in Kirklees, has not changed the timing of his school's test.
"Such a tight time-frame would be very difficult indeed," he said.
However, some areas with selective secondary education do make results available. These include Lincolnshire, Gloucestershire and Medway.
Wallington County Grammar School in the London borough of Sutton, which administers its own 11-plus, said at least 300 more children had taken its entrance exam this year after it changed its system to make results available to parents early.
Dr Martin Haworth, the headteacher, said: "If you look at the admissions code, it more than suggests that this change should take place.