Downing Street has insisted the NHS coronavirus app is working as it was “designed”, and rejected mounting calls to act to prevent a surge in workers and medics being forced into self-isolation over coronavirus contacts.

No 10 declined to shorten the month-long delay between when most restrictions end on so-called “freedom day” on Monday and the quarantine rules being eased for the double-jabbed.

Employers have warned of a looming staffing crisis, which could compound pressure on the NHS, with some staff already having been asked to put holidays on hold due to the rising number of patients.

Amid warnings of a “pingdemic”, fully-vaccinated individuals will be exempt from having to quarantine over close contacts, but the change will not be introduced until August 16.

Ministers are examining whether to make the NHS app less sensitive, with 530,126 alerts having been sent in England and Wales during the first week of July.

But Downing Street appeared to dampen hopes that any changes could be made to reduce the number of pings in the coming days.

“We keep things under review but the app is doing what it is designed to do,” a No 10 spokesman said.

Asked if the August 16 relaxation of rules could be brought forward, the spokesman said: “It is as the Health Secretary set out in the House last week.”

But he did not deny that staff in some sectors could be offered an exemptions after the British Meat Processors Association said ministers had vowed to step in if staff shortages continued in the industry.

The spokesman also sought to alleviate concerns that people were being asked to self-isolate because they have been pinged through the walls of their house, but could not rule it out.

“We’re confident that that is not contributing to large numbers of individuals being asked to self-isolate,” he said.

“The app uses low-energy Bluetooth and its signal strength is significantly reduced through things like brick walls, so therefore it is highly unlikely that through brick walls would lead to an alert.”

England’s chief medical officer Chris Whitty has warned that the number of people being treated in hospital with Covid-19 could reach “quite scary” levels within weeks.

The Royal College of Anaesthetists and the Faculty of Intensive Care Medicine issued a joint call to exempt all double-jabbed NHS staff from isolation over close contacts.

“The risk of patients contracting Covid from vaccinated healthcare staff is minimal compared to the damage that patients could suffer by having their treatment delayed,” a statement said.

“Without this exemption in place, the NHS will not be able to address the waiting lists. We encourage the Government to not wait until August to free vaccinated healthcare workers from the isolation rules – we need this to happen now.”

Chris Hopson, the chief executive of NHS Providers, said the hospital trusts the organisation represents are increasingly concerned over dealing with the care backlog “with large numbers of staff unable to work”.

“We know that national leaders are working hard to find a solution to this problem. The key is that this solution is delivered as a matter of urgency,” he added.

Health bosses in Sunderland have asked staff to consider postponing holidays to help the trust as it comes under “extreme pressure” due to a surge in coronavirus cases.

Rail, Maritime and Transport union (RMT) general secretary Mick Lynch warned that Monday “will see a surge in workers pinged with a self-isolation instruction next week”.

“Even at this late stage, the Government, the train operators and the bus companies should issue a clear, legally backed instruction that levels up the rest of the UK to the safety standards that will remain in force in Wales and Scotland,” he added.

Pubs and restaurants were also issuing warnings over possibly having to close their doors due to the level of pings.

UKHospitality chief executive Kate Nichols said the industry is facing “significant staffing challenges” with up to as many as a fifth of staff isolating at any one time.

“Without better intervention, operators will continue to be forced to reduce their operating hours or to close venues completely, missing the opportunity to begin on their road to recovery,” she said.

“We urge the Government to move quicker on this issue to prevent the summer being cancelled and vast swathes of the population unnecessarily confined to their homes.”

Punch Taverns founder Hugh Osmond called for those pinged on the NHS Covid-19 app to be allowed to go back to work if they get a PCR test that returns negative.

“It is absolutely chaos, and clearly the app really isn’t fit for purpose because people are getting pinged all over the place and the vast majority do not ever test positive, let alone be ill,” he told BBC Radio 4’s Today.

Sir Jonathan Montgomery, the former chair of the ethics advisory board for the NHS Test and Trace app, said he would change the “consequences of being pinged”.

“When the app was designed, we didn’t have the ability to reliably home test, we didn’t have very many people jabbed, and the big worrying thing about this virus is that you can pass it on before you know you have it,” the professor of healthcare law at University College London told LBC.