He says the balance of risk has changed, and schools are struggling to stay open.
Williamson says schools in England will remain closed from Friday until further notice.
But the children of key workers, and children who are vulnerable, will be able to stay.
He says he will put in place a voucher scheme to make up for free school meals.
Just before the announcement, Scarborough TEC released a statement saying that it would close from 5pm on Thursday 19 March and move to supported online learning from Monday 23 March.
The campus will be accessible from Monday 23 March from 9am-5pm, Monday to Thursday, and 9am-4pm on Fridays for anyone who wishes to use the library for study purposes.
Any exams that are scheduled to take place will be postponed, and all work placements will be cancelled from Monday 23 March until further notice, it said.