Schools in England have been urged by the government not to send whole bubbles of pupils home just because one tests positive for Covid, amid a growing row about the policy’s enforcement and overhaul. In a move that sparked anger from school leaders, Downing Street said decisions about which pupils should be sent home can be made on a “case-by-case basis” and that schools needed to better “understand this”. Pressure is growing on ministers to urgently scrap or change the policy on bubbles for pupils, given the number currently off school is 375,000 – a 400% rise in the past month. The Guardian revealed on Monday that they were planning to overhaul the current system and revert to mass testing in schools to prevent children in large bubbles – sometimes numbering more than 200 – all being forced to miss out on in-person teaching because of a single Covid case. But the education secretary, Gavin Williamson, signalled on Wednesday that the change was unlikely to be introduced before most schools broke up for the summer. He said changes to bubbles would not come into force before the final stage of the government’s roadmap, due to be implemented on 19 July – days before many schools in England close for the holidays – though he admitted there were “still too many children” having their education disrupted. About 200 schools have been part of a trial of daily contact testing to monitor how much infections are passed on, but will have to revert to the current policy as the pilot ended on 30 June. Given there are just nine weeks until term begins for most pupils in September, Labour has pushed for Williamson to “act now” to get children back to the classroom quicker and give schools time to prepare for any change in restrictions. Kate Green, the shadow education secretary, said changes not coming into force until 19 July would “create more chaos for schools and families”. She also called for an end to the “drip-feed of information, which is wreaking havoc with children’s educations”. Boris Johnson’s spokesperson sought to clarify the current advice to schools, stressing “it is not a requirement necessarily that whole school bubbles needed to isolate” and saying the government was “working with schools so they understand this guidance”. But Downing Street was accused of lecturing headteachers on the rules. Geoff Barton, the general secretary of the Association of School and College Leaders, which represents most secondary state school heads in England, said schools were “well aware” of tracing requirements but that the number of students forced to isolate “can very quickly escalate according to the circumstances in each case”. He added: “What headteachers and principals need from the government is clarity about how it intends to change the rules to end the ongoing educational disruption.” Conservative MPs also piled pressure on the government to act faster. Robert Halfon, the chair of the Commons education select committee, warned there could be “a generation of ghost children” created and called for mobile testing units to be created for schools before September. Mark Harper, the chair of the Covid Recovery Group, said he was unsure why the bubbles policy could not be changed speedily, arguing it would continue to “cause a huge problem for the rest of term”. In Gloucestershire, 8% of students are being forced to isolate, the Conservative MP for Gloucester, Richard Graham, complained. Another Tory MP, Suzanne Webb, said reforms to the bubble policy “can’t come soon enough”. Richard Sheriff, the chief executive of the Red Kite Learning Trust, which has schools in North and West Yorkshire, said there was a growing sense among school leaders that they would have to stop sending pupils home, or children would never recover. But he warned against doing anything too hasty, preferring to wait until September to introduce new measures. “This is not an overnight thing to do. I don’t think dashing to get rid of bubbles in the last few weeks of term is a good idea,” he said. Jon Richards, the head of education for Unison, called for mandatory face coverings in schools to return and for bubbles to be made smaller.