Almost 10,000 people a day in the UK are contracting coronavirus, the health secretary, Matt Hancock, has warned, as Scotland’s first minister requested urgent talks with the UK government to consider further tightening social restrictions. Hancock said the latest surge in infections was still significantly lower than the 100,000 a day estimated during the spring and urged people to download the newly released NHS contact-tracing app to “make the country a safer place”. Speaking to Sky News, he said: “Yesterday we had a figure that there are over 6,000 people who have tested positive in the previous 24 hours. That is comparable to the highest levels in the peak in terms of the number of people who were tested positive but back then we estimate through surveys that over 100,000 people a day were catching the disease, but we only found around 6,000 of them through testing. “Now we estimate that it is under 10,000 people a day getting the disease – that’s too high but it is still much lower than in the peak – and through the mass testing we have … we found yesterday over 6,000 of them.” Nicola Sturgeon wrote to Boris Johnson on Thursday calling for urgent talks on tighter lockdown restrictions to tackle the spread of the virus, pointing to warnings from scientists on Wednesday that measures do not go far enough to control the spread. “While all four governments announced new restrictions yesterday, there is clearly a significant strand of scientific opinion to the effect that bringing R back below 1 and the virus back under control will require measures beyond those which any of us have so far announced,” she said. “In my view, there is considerable force in that opinion. It is also the case – and we know this from our experience earlier this year – that acting quickly and decisively against the virus is essential.” She said there was “nothing to be gained – and potentially much to be lost, including lives – from delay”. Hancock acknowledged there had been disagreements between scientists about the route to take to tackle the virus – including some such as the University of Oxford’s Carl Heneghan, who had argued the restrictions went too far. “There are reasonable disagreements between scientists and the role of Chris Whitty as chief medical officer is to try to synthesise all of that scientific advice and present the best possible analysis and then we take decisions based on that advice, listening to people right across the board,” he told BBC Radio 4’s Today programme. Hancock was speaking after the NHS’s Covid contact-tracing app was launched in England and Wales on Thursday. International examples show take-up rates of similar apps at between 10% and 30%, a far cry from the NHS app target in April of 80% of smartphone users. The app, which uses Google and Apple technology, will alert the user if they have been within 2 metres for more than 15 minutes of somebody who has tested positive, and who also has the app. Other functions allow the user to check in at a venue that displays a QR code, rather than having to give staff their details. The user can book a test and will be given advice on self-isolation if necessary, including a daily countdown, so they know when they can leave home again. Pilot studies on the Isle of Wight, in the London borough of Newham and among NHS volunteers have shown that downloads of the app are similar to the rates in other countries. The highest rate, of about 30%, was in the Isle of Wight, where an earlier trial meant people were already used to the idea of a contact-tracing app. In Newham the take-up was close to 10%.