Secondary schools in England look set to open up to a week late this autumn term as millions of teenagers must be tested twice for Covid.
The Department for Education has said headteachers can "stagger" the return of classes to give schools time to begin the new testing regime.
Any youngster found to have Covid will have to self-isolate. Their close contacts will be traced and tested, and asked to quarantine, if they too are positive.
Although schools have the option of beginning checks the week before September 1, children and staff on scheduled breaks mean many school leaders with no choice but to postpone schools fully opening.
But Labour has attacked the Government's "chaotic" as youngster have already missed an average of 115 days of school since the outbreak of Covid.
Kate Green, Labour’s Shadow Education Secretary, said: “The Conservatives chaotic, last-minute approach is damaging children’s education. Parents would rightly expect Ministers to have learnt from their mistakes over the last year, but once again families are being treated as an afterthought.
“After two years of disrupted education each day in school matters. The Conservatives’ systematic refusal to plan ahead is just not good enough."
Mr Williamson got rid of the bubble policy, which saw classes of children forced into quarantine when a child tested positive, at the end of last term.
Education and health chiefs see mass testing, which is part of the Government's overall plan to swerve a winter surge of the virus, before and throughout term as less disruptive.
Geoff Barton, general secretary of Association of School and College Leaders, said parents were like to be angry about the move, but it was a complex operation for schools.
He said: “If you have nine million children going back into school, having been mixing through the summer, you can see the need to test them on site. Logistically it will be challenging.
"We thought we could focus on the norm of education and already we have the spectre of disruption. Parents may rightly feel frustrated.”
Paul Whiteman, general secretary of school leaders’ union NAHT, said: “Schools are simply following government guidance here.
"The government has once again asked secondary schools to effectively transform themselves into Covid testing centres ahead of the new school term. The reality is that there is very little in the way of meaningful support being provided for these schools and so most are having to re-deploy existing staff to oversee these complex arrangements at the start of term.
"This is a public health task, and we have repeatedly called on the government to do more to provide public health staff to implement on-site testing.
"The government’s guidance has always stated that schools can stagger the return of pupils across the first week to manage this. Staff in these schools will be working as hard and quickly as they can to ensure all pupils receive both tests the government says they should have prior to returning.”
Ministers announced last week that classrooms will be fitted with air quality monitors to combat the spread of Covid with better ventilation.
Families will be asked to test their children twice weekly for the virus until the end of next month when the policy will be reviewed.
Steve Chalke, chief executive of one of the biggest academy trusts, Oasis, told the Sunday Times the Government's approach was "all last minute again".
He said: "Head teachers have called for months for a way of opening schools and keeping them open to avoid a third year of academic disruption to children.”
A Department for Education spokesperson said: “Our priority is to ensure settings are able to deliver high-quality, face-to-face education to all pupils.
“As our guidance stated in June, and to ensure all pupils receive the education they deserve with minimal disruption, settings may commence testing from three working days before the start of term and can stagger the return of pupils across the first week to manage this process.”
