Labour has expressed concern at coronavirus lockdown measures being eased at the start of June after ministers conceded that a key part of the test-and-trace regime to contain new outbreaks, a phone app, would not be ready for weeks. The health secretary, Matt Hancock, announced that anyone over the age of five with coronavirus symptoms would be eligible for a Covid-19 test. The news is expected to lead to a surge in people visiting the gov.uk website to book home test kits or drive-through appointments. Until now, eligibility was limited to certain groups including key workers, those aged over 65, people who could not work from home, or people who lived with someone from one of these groups. But there are fresh worries about the NHS phone app, which is designed to be downloaded by millions to curb the spread of Covid-19, as the organisation representing local public health leaders said it was “disappointed” at the level of government engagement on the issue. Amid ongoing questions about the scheme, England’s deputy chief medical officer acknowledged that the country needed to go “bigger and faster” when it came to testing. While ministers announced on Monday that they had exceeded the 18,000 target for applicants to become contact tracers in the new system, with more than 21,000 now confirmed, the national rollout of the app has been held up. Last week, Hancock said it would be ready by mid-May. But answering questions at the daily Downing Street press conference, Dominic Raab, the foreign secretary, said this would now happen “in the coming weeks”. The app, which is intended to notify authorities of new Covid-19 cases so people who have been in contact with them can be contacted and self-isolate, is being tested on the Isle of Wight. It has been downloaded by about 60,000 people there, just under half the island’s population. Raab was unable to confirm that the app would be ready for national use by 1 June, the earliest date for the so-called stage two of the lockdown easing, which will see some primary pupils return to school, and the reopening of some non-essential shops. “In terms of the app, it’s still our intention to roll it out across the country for everyone to use in the weeks ahead. I can’t be any more precise at this stage,” he said. “But, as I’ve said before, we’re making pretty good progress with it.” Raab added: “We are learning all the way as we go through this pandemic, not just on the scientific side but on the innovation, that we need to get a grip on it.” Making a statement earlier in the House of Commons, Hancock said he was “ready and preparing for rolling out that system”, but gave no date. Jonathan Ashworth, the shadow health secretary, said he was concerned at the new timetable. “Ministers promised tracing would be in place by the middle of this month,” he said. “The deadline has now slipped again even though a tracing service is vital for a safe easing of lockdown restrictions. The government’s failure to bring in a functional test, trace and isolate regime exposed yet again the slowness of ministers to get a grip of this crisis.” Separately, in a statement released on Monday, the Association of Directors of Public Health said its members would work closely with the government to implement the new tracking regime, but listed a series of areas where it had concerns. The organisation was “disappointed at the limited extent the government has involved local government in the development of all aspects of the test, track and trace programme”, the statement said. Among a series of recommendations, the statement urged greater cooperation, more localism and efforts to avoid duplication in operating the new system. Downing Street had indicated earlier that the introduction of the app might not be necessary either for the new system to operate, or for the lockdown to be eased further. “It is possible to do track and trace work separately to the app, and that’s obviously something that happened previously. And it’s perfectly possible to do that again,” Boris Johnson’s spokesman said. Asked whether the app was necessary for the changes on 1 June, he said that this decision would be based on the five tests the government has set, including the rate of infection. Prof Jonathan Van-Tam, the deputy chief medical officer for England, speaking alongside Raab at the briefing, echoed this point, saying the app was “one part of the test and trace system” and that a more vital element was the work of the contact tracers. But as the government announced an expansion of testing for anyone with possible coronavirus symptoms, he agreed with a questioner who asked whether some test results were coming back too slowly. “From that perspective you are absolutely right that we need to do it bigger, and faster, and as fast as we can,” he said. “And we are sending a clear message as scientists, that it needs to be fast, and we have to work as hard as we can to improve the timeliness of the testing system as we go along.” At the press briefing, Raab stressed that the 1 June date for the next stage of the easing was not confirmed: “We’ve always said, of course, that the steps that we might take with step two, will only ever be taken at the earliest on 1 June. So we’ve not committed ourselves to anything at this point in time.”