The definition of a critical worker should be "urgently" reviewed to reduce pressure on teachers, a committee of the House of Lords has said.
The committee said that the definition should be included in regulations rather than just in the guidance, and be scrutinised by Parliament.
It highlighted that news reports have been warning that an expanded definition of "critical worker" has resulted in schools seeing more pupils in school compared with the first lockdown.
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The committee warned that this situation is not only hampering efforts to limit the spread of the virus, but also putting pressure on teachers.
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In its report, the committee said: "This not only works against the aim of limiting the spread of infection but is also detrimental to educational standards as teachers struggle to cope with teaching in person and online at the same time."
The warning comes after the Chartered College of Teaching said last week that 80 per cent of teachers reported that attendance had increased "greatly" compared with the first lockdown.
Committee member Baroness Watkins of Tavistock said: “We echo concerns in recent news reports which highlight the pressure teachers are under to effectively support both children at school as well as those attending online.
"This is due to higher numbers of children at school than in previous lockdowns because the definition of 'critical worker' has been expanded.
“We consider it necessary to urgently re-examine this issue to reduce the pressures on teachers and ensure quality teaching for all children, both those at school and those attending online.
“We ask the House for the definition to be reviewed urgently and included in regulations so that it can be subject to scrutiny by Parliament.”
However, the Department for Education has said schools should not limit the number of children of critical workers who can attend. although it also clarified that children of key workers should stay at home "if they can".