Scores of councils in England say they cannot guarantee primaries will reopen on 1 June, throwing government plans to get pupils back to school into chaos.
Only 20 of 99 councils to respond to a BBC Breakfast survey said they were advising schools to open more widely on Boris Johnson's target date.
Of the 99 who responded, two thirds (68), could not guarantee schools would reopen to Reception, Year 1 and Year 6.
It comes as the government prepares to publish scientific advice on its plan.
On Thursday the governments of Scotland and Northern Ireland announced plans for a phased return to school for pupils, starting in August.
Ministers have been insisting that they would only be calling on schools in England to reopen in June if the scientific advice said it was safe to do so.