More than 500,000 volunteers have signed up to support the NHS in helping vulnerable people who have been told not to leave their homes during the coronavirus crisis.

Nearly five people per second enlisted in the government’s new volunteering scheme in the hours after the health secretary, Matt Hancock, launched a call on Tuesday for 250,000 people in England to help bolster the NHS response to the Covid-19 pandemic.

Play Video 1:10 Boris Johnson: 405,000 NHS volunteers signed up in 24 hours – video

Overnight the number of volunteers who had pledged support topped 170,000, and as the day went on the target was smashed. “That is already, in one day, as many people as the population of Coventry,” said Boris Johnson in the daily Downing Street press conference. The figure now stands at 504,303.

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The overwhelming response has prompted the NHS to extend its target to recruit 750,000 volunteers in total. Those volunteers who have already signed up will start next week.

As the coronavirus death toll in the UK rose to 422 people as of 10.10am on Wednesday, the government called on fit and healthy adults to deliver vital supplies such as food and medicines to up to 1.5 million vulnerable people, drive them home after being discharged from hospital and make regular phone calls to those in self-isolation.

Nearly 12,000 recently retired NHS staff came forward to rejoin the frontline following a separate call for help. The government has announced plans to set up a makeshift hospital with capacity for 4,000 beds at the ExCeL centre in east London.

Announcing on Wednesday morning that the government’s volunteering scheme was two-thirds of the way to reaching its target just 15 hours after it was set in motion, NHS England’s national medical director, Stephen Powis, said he was “bowled over” by the “astonishing” response.

“Yesterday we sent out a call to arms for an army of NHS volunteers, looking for a quarter of a million volunteers, and I can say that overnight we’ve already had 170,000 people sign up ... It’s an absolutely astonishing response,” he told BBC Breakfast.

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Asked if he had expected such support, he replied: “I think at times of crisis, people come together. And the vast majority of people in this country are doing what the government has asked us all to do. But it’s important that everyone does that as that will save lives.

“I know there’s vast numbers of people looking to help neighbours, vulnerable people who live close by, so no it doesn’t surprise me at all. In times like this, as the chief medical officer has already said, we see outbreaks of altruism, people wanting to help, so it’s a wonderful response in the same way that all those doctors coming back, nurses coming back. I’m bowled over by it.”

Quick guide UK lockdown: what are the coronavirus restrictions? Show Hide What do the restrictions involve? People in the UK will only be allowed to leave their home for the following purposes: Shopping for basic necessities, as infrequently as possible

One form of exercise a day – for example a run, walk, or cycle – alone or with members of your household

Any medical need, to provide care or to help a vulnerable person

Travelling to and from work, but only where this is absolutely necessary and cannot be done from home Police will have the powers to enforce the rules, including through fines and dispersing gatherings. To ensure compliance with the instruction to stay at home, the government will: Close all shops selling non-essential goods, including clothing and electronic stores and other premises including libraries, playgrounds and outdoor gyms, and places of worship

Stop all gatherings of more than two people in public – excluding people you live with

Stop all social events, including weddings, baptisms and other ceremonies, but excluding funerals Parks will remain open for exercise, but gatherings will be dispersed.

People can join the scheme in four different roles, including as a community response volunteer, which involves “collecting shopping, medication or other essential supplies for someone who is self-isolating, and delivering these supplies to their home”.

Patient transport volunteers will support the NHS by driving discharged patients to their homes, and NHS transport volunteers will move equipment, supplies or medication between sites. Other volunteers will provide support calls to elderly people who are in isolation and at risk of loneliness.

Volunteers, who must be over 18, fit and healthy and able to pass an enhanced DBS check, will be directed to tasks via a responder app that they can switch to say they are “on duty” when available.

Robert Jenrick, the housing and communities secretary, told BBC Breakfast: “I know there are hundreds of thousands, if not millions of people out there who would like to support us during this time and support the NHS.

“There will be lots of different opportunities available from helping deliver medicines and food to the elderly and vulnerable who we’re asking to stay at home, being volunteer drivers to get supplies to the frontline or to take people into hospital, or working in hospitals obviously in non-clinical roles.”

Asked if the scheme went against advice to stay at home and how the government would keep volunteers safe, Jenrick said: “The government’s guidance is to stay at home unless you’ve got a reason to be going out. If you’re doing something absolutely essential for fighting the virus, like volunteering in this very organised way, then obviously that’s different. But we want to keep those individuals safe, they’ll receive the training, the support and the equipment that they’ll need to carry out those roles.”