The five proposals were contained in an eight-page paper written by officials in Michael Gove’s Cabinet Office.
It was presented to the Covid-19 Operations Committee which delivers Britain’s policy and operational response to the virus.
If adopted they would go further than the government’s stated aim to end current isolation rules end in the autumn.
Children’s Commissioner Dame Rachel de Souza has said there is an urgent need for children to get back to normal.
She branded lockdown restrictions a ‘real trauma’ for many young people.
A spokesperson for the government told the Telegraph: ‘Throughout the pandemic we have always sought to keep pupils in school and protect their education.
‘As the Education Secretary has said, we expect to be able to confirm plans to lift restrictions and bubbles as part of Step 4 [in the roadmap out of lockdown].
‘However, no final decisions have been made on this or future testing and isolation requirements.’
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