GCSE and A-level students in England may have to sit externally set tests as part of their teacher-assessed grades this year, according to new guidance for how qualifications could be awarded after formal exams were cancelled.

In a letter to exams regulator Ofqual, education secretary Gavin Williamson on Wednesday said students should be assessed as late as possible in the school year to ensure they remain motivated to study.

Assessments for Year 11 and 13 students in England were left in limbo last week after the government closed schools, cancelled exams and announced students would be graded by their teachers, in a series of U-turns by the Department for Education.

Mr Williamson is now under pressure to deliver a workable alternative to exams that does not repeat the failure of last year, or unfairly disadvantage students who have had their education disrupted by the pandemic.

In his letter, he said a “breadth of evidence” should inform grades, and that civil servants should “explore the possibility of providing externally set tasks or papers” so teachers could use them in their marking.

He suggested that students are graded according to what they have learnt, rather than parts of the curriculum they have unable to study, and confirmed that the government would not use an algorithm to “set or automatically standardise anyone’s grade”.

Ofqual will next week launch a two-week consultation in response to Mr Williamson’s letter.

Newly appointed chief regulator Simon Lebus said this year’s assessments could not have the same “degree of reliability” as standardised national exams. But he said regulators would work rapidly to ensure assessment was as “manageable as possible” for teachers, with a “clear quality assurance” process.

The Association of School and College Leaders, a union, said the letter set out “broad and sensible parameters” for how children could be assessed fairly.

“One of the key issues, however, will be precisely how any system of externally set assessment would work and how this can be done in a way that ensures fairness for students,” said Geoff Barton, general secretary of the ASCL.

In response to a controversy over inadequate meal provision for disadvantaged pupils during lockdown, Mr Williamson told parliament’s education select committee that the government would “name and shame” companies found to have sent poor quality parcels to children.

He added that a national scheme for procuring vouchers would be available from next week, but schools would “still have the option of doing locally procured vouchers” and would be refunded by the government “if that’s what they want to do”.

Speaking alongside new education permanent secretary Susan Acland-Hood on Wednesday, Mr Williamson also said that the DfE was establishing safety measures to allow pupils to return to the classroom as soon as possible.

He added that the government planned to extend rapid coronavirus testing, which is currently only distributed to secondary schools, to primary school staff from next week, and hoped to extend testing to all pupils.

The education secretary added he would “fight tooth and nail” to prioritise teachers, support workers and special school staff in the next phase of coronavirus vaccinations.

Mary Bousted, the general secretary of the National Education Union, which represents teachers, welcomed the commitment, but said the problem of community transmission between children and their families remained.

“The devil is in the detail and the government has a poor track record on delivering on its promises,” she said.