England’s coronavirus testing strategy has been been criticised as “reckless” amid plans to end the free provision of rapid tests and relax the monitoring of cases from abroad.

Families and businesses will have to pay for lateral flow tests from next year in an overhaul of Downing Street’s approach to the pandemic.

More than 95m of the 30-minute tests have been used since they were made freely available in England from April. Reported to cost £5-£30 each, they have identified more than 620,000 cases, mostly in people without symptoms but who could still transmit the virus.

Mayors, teaching unions and directors of public health said charging for lateral flow tests was a “backward step” that threatened to throw schools back into chaos, accelerate the spread of the virus and deepen health inequalities.

Paul Whiteman, the general secretary of the school leaders’ union NAHT, said: “The best way to minimise disruption to children’s education is to keep the number of Covid cases in school as low as possible. Testing is critical to this. Removing free access to Covid tests while cases are still high would be reckless. Nor can schools bear the cost of paying for tests for all their pupils and families.”

Anyone without symptoms can order the tests online although they are used primarily in schools, care homes and the NHS. They have detected nearly 173,000 positive cases in nurseries, schools and colleges and more than 35,000 cases in care homes since January, according to a Guardian analysis.

Andy Burnham, the mayor of Greater Manchester, said making lateral flow tests paid-for was a backward step, adding: “Charging for lateral flow testing in our view could only lead to the increased spread of the virus and deepening those inequalities that we’ve seen all the way through this pandemic.”

The winter plan, published this week, said lateral flow devices would continue to be provided for free “in the coming months” but thereafter “universal free provision of LFDs will end, and individuals and businesses using the tests will bear the cost”. The document said the government would “engage widely” on how chargingwould work because rapid tests “could continue to have an important, ongoing role to play in future”.

There was no detail on how schools or care homes would be able to fund the provision of lateral flow tests once they are no longer free. A Department of Health and Social Care spokesperson said: “LFDs are a crucial measure to stop the spread of Covid-19 and that’s precisely why we have confirmed that we are extending the free provision of these tests.”

Kevin Courtney, joint general secretary of the National Education Union, said: “If government wants regular testing to take place in the long term then erecting financial barriers will mean many people simply won’t engage, which is bound to lead to greater spread.”

Use of lateral flow tests has fallen from a high of about 7.5m a week in spring, though nearly 6,000 cases were picked up from 6m tests as schools returned in the week to 8 September.

Jamie Driscoll, the North of Tyne mayor, said expecting people on low wages to pay for rapid tests to get the all-clear to go to work was “the exact opposite of levelling-up”. He said it was “the most counter-productive penny-pinching you can imagine”, adding: “When you’ve got a communicable lethal disease like Covid, why on earth would you roll back the public health benefits of testing?”

Prof Kate Ardern, the lead director of public health in Greater Manchester, questioned why people should have to pay for coronavirus tests when tests for other diseases, such as tuberculosis, were free on the NHS. “Anything that potentially deters people from continuing to do [testing] – and a charge does do that – then that is potentially a little bit worrying,” she said.

Prof Dominic Harrison, the director of public health in Blackburn-with-Darwen, which has had the most Covid cases per capita since the start of the pandemic, said it was “critical” that testing remained free for those most at risk

“Anything that puts a barrier up to community level testing in high-risk communities, which we know are often the most low-income communities, will increase the risk of further transmission and of course hospitalisation and mortality,” he said.