Headteachers were told to order lateral flow tests by 5pm on Tuesday to avoid a two-week wait for their arrival.
In an email to school leaders from the Department for Education sent on Tuesday, the Government said that schools had been “invited to order tests before Christmas and will have received these in advance of pupils returning”.
But the DfE added that orders for test kits received by 5pm would “be scheduled for delivery during next week” but that orders placed after 5pm would be delivered the following week beginning January 17.
On Twitter, Education Secretary Nadhim Zahawi said that all schools and colleges that had ordered test kits for the new term “have received them, we’ve delivered a massive 31 million kits”.
“Thanks to everyone supporting on-site testing so children and teachers can be in the classroom for face-to-face learning, where they want and need to be,” he added.
Geoff Barton, general secretary of the Association of School and College Leaders, said: “We have been assured by the Department for Education that there will be enough lateral flow test kits for schools and colleges.”
“We have received a couple of messages from members about issues over the supply of test kits to their schools and we have raised these with government officials.
“It is clearly imperative that schools and colleges have enough test kits or otherwise it will be impossible for them to follow the government guidance on providing these kits to staff and eligible pupils for home testing.
“We will continue to monitor the situation.”
A DfE spokesperson said: “All schools were invited to place orders for additional test kits before Christmas, with around 31 million tests delivered to education settings in the final weeks of term, so schools should have sufficient supplies of lateral flow tests.
“A further 17.6 million test kits will be delivered by the end of next week, and schools can request an emergency replenishment of tests if required.”
The email also suggests that secondary pupils should be “strongly encouraged to continue testing twice weekly at home” following their one on-site test at the start of term, and to report results to NHS Test and Trace and to their school.
The news comes amid fears over shortages, with No 10 recognising there were periods during recent days when tests were unavailable online during the wave of Omicron cases.