New cases of coronavirus are doubling almost weekly across England, figures revealed, as Birmingham became the biggest local authority to announce a tightening of lockdown measures and health officials flagged “worrying signs” of infections in elderly people. The measures to be introduced in Birmingham next week mean more than 7.3 million people – 11% of the UK population – will be living in areas affected by some level of local lockdown, according to a Guardian analysis. After signs that the number of virus infections is accelerating sharply, the former UK government chief scientific adviser Sir David King urged ministers to improve the NHS test-and-trace system. He said England was on a “knife-edge”. King’s warning came as the latest figures showed another huge surge in UK positive cases on Friday – up to 3,539, compared with 1,940 a week ago. While the number of people dying from Covid-19 remains low, there has been a steady increase in the numbers of patients in hospital in recent weeks. On Friday, it stood at 863, a rise of 120 from the week before. Yvonne Doyle, the medical director of Public Health England, said there were signs of a worrying trend. “Although younger people continue to make up the greatest share of new cases, we’re now starting to see worrying signs of infections occurring in the elderly, who are at far higher risk of getting seriously ill.” Deenan Pillay, a professor of virology at University College London, said available data showed less than 50% of people being asked to isolate were doing so properly. With infection rates rising, the West Midlands councils of Birmingham, Sandwell and Solihull announced that from Tuesday, they will no longer allow their 1.6 million residents to mix with different households. The leader of Birmingham city council, Ian Ward, said the measures were needed to curb an increase of hospital admissions with Covid-19 and an increase in cases in care homes. “The spread appears to be primarily occurring through social interactions, especially private household gatherings, and workplaces where social distancing is not being observed,” he said. Liverpool had also been added to the government’s coronavirus watchlist of areas of concern after a fourfold rise in confirmed cases in the last fortnight, the city’s public health officials said. And Sir Richard Leese, the leader of Manchester city council, said the city would have to consider “a full lockdown” if the number of Covid 19 cases did not start to go down. Holyrood also announced that restrictions on private indoor gatherings across the west of Scotland had been extended to Lanarkshire. The extent of the rise in cases was set out in data published by scientists at Imperial College London, who calculated that infections in England were now doubling every 7.7 days. But with more people needing tests, further evidence emerged on Friday to suggest the system is struggling to cope. Hundreds took to social media to voice their anger and complained to their MPs as the 119 helpline rang out and the NHS test and trace website reported no tests were available in person or by post, or suggested testing stations hundreds of miles away. People left frustrated included paramedics, teachers and doctors who are being forced to self-isolate, perhaps unnecessarily. Barry Worthington, from Wigan, said he had Covid symptoms and could have caught the virus from his grandson who returned from school with a persistent cough. But he could not get a test on Friday as the 119 helpline rang out, and online he was offered an appointment 334 miles away in Aberdeen. “They were properly concerned,” he said. “She went and had a chat with a supervisor, came back said there are no tests in the country at this time.” Fergus Simpson, a PhD student who is looking after an elderly aunt in Guildford, described the system as shambolic. He had been with his sister who tested positive on Tuesday but has been unable to get a test. He said it took two days for contact tracers to ask his sister for her contacts and they took addresses but no phone numbers or emails. None of the people she told them about had been contacted, he said. “It’s a shambles. I’m watching Boris saying we have a world-beating test-and-trace system and attacking naysayers for whining that it isn’t working. Well it isn’t working and I am evidence of that.” King, who chairs the Independent Sage group of scientists, said there was now a “knife-edge opportunity to improve testing, tracing and isolation to get cases down, giving us a good chance of being able to get together with family at Christmas”. His group described the NHS test-and-trace system as “flawed, with an illogical focus on numbers tested”. A spokesperson for the Department of Health and Social Care said: “NHS test and trace is working, our capacity is the highest it has ever been and our laboratories – the largest network assembled in British history – are processing more than a million tests a week. We are seeing a significant demand for tests, but more booking slots and home testing kits are available daily for those who have coronavirus symptoms.” They said the department was investing £500m in next generation tests and expanding capacity to 500,000 tests a day by the end of October, but did not refer to the government’s “moonshot” attempt to spend £100bn testing 10 million people a day by early 2021.