Former health professionals could be brought out of retirement under emergency plans being considered by the government to combat the spread of coronavirus.

News of the potential “Dad’s army” deployment comes as NHS bosses warn that the service will struggle if Covid-19 takes hold in Britain.

Yesterday a further three people in England tested positive for the virus, bringing the total number of confirmed cases in the UK to 23. Two of the patients had recently travelled back from Italy, while the other had returned from Asia, according to the chief medical officer, Prof Chris Whitty.

The three cases – in Gloucestershire, Hertfordshire and Berkshire – are being investigated, and any individuals who had contact with them are being traced.

The update came as the health secretary, Matt Hancock, geared up to launch what the Department of Health described as an “enhanced government approach” to pandemic preparation in a bid to assure the public that it had a grip on the situation.

The plans will a designated ministerial virus lead for every government department, a cross-government “war room” of communications experts and scientists ahead of a new public information campaign and an increase in the number of Cobra emergency meetings.

Currently the UK is in the “containment” phase, where isolated cases are hospitalised and detailed tracing of those they have come into contact with is carried out. However, if the virus begins to spread the Department of Health said the next phase could see broader measures to keep the public safe and relieve pressure on the NHS.

These could include the emergency registration of retired health professionals, the introduction of emergency indemnity coverage for healthcare workers providing care or diagnostic services and a relaxation of rules around staff-to-pupil ratios in schools and nurseries.

The government is also considering encouraging more home working and discouraging unnecessary travel as part of a “social distancing” strategy that it says would delay the peak of the outbreak until later in the year, when warmer weather could help in combating the virus.

Boris Johnson, who will chair a Cobra meeting tomorrow after criticism of his response so far, warned: “Coronavirus may very well be a challenge in the weeks and months ahead. But I have no doubt that with the help of the NHS and its incomparable staff this country will get through it – and beat it.”

But two NHS chief executives, who spoke to the Observer on condition of anonymity, warned that the NHS will struggle if there is a major outbreak because it has too few beds, staff and specialist equipment.

“If you have a coronavirus outbreak it will be a nightmare,” one said. “How will we create the extra capacity that we will need? All hospitals are already full. It will be really, really difficult if we get loads of people with this.”

The boss of another trust said: “About 17% of people who contract the virus need some sort of medical intervention. So if this properly catches hold you have a [huge] increase in the number of people coming through the NHS’s door, and then everything falls over.”

School closures could severely deplete the number of staff working in hospitals, because they would have to stay at home to look after children there, one of the chief executives warned.

“The key for a lot of staff is the schools – if they are closed, we are in trouble. And if staff themselves are isolated or refuse to work, we are in trouble. With no spare staff and extra pressures, we would really struggle.”

Rachel Harrison, national officer for the GMB union, which represents NHS ambulance crews, said there were concerns about whether its members had the relevant protective equipment. “The pressure on the service is already immense,” she said. “They are constantly getting called out to things they shouldn’t be called out for.”

Jonathan Leach, honorary secretary of the Royal College of GPs, said the NHS had done well to contain the virus in the UK so far, and was well-prepared should the situation escalate. “We have a good track record of dealing with emergency situations, and there is currently no reason to think this one should be any different. We will, of course, be monitoring the situation closely.”

But Susan Crossland, president of the Society for Acute Medicine, disagreed: “While the emergency planning measures put in place specifically for coronavirus have been good, the wider picture is one of grave concern. One of the huge problems we will see in the event of a widespread outbreak is a complete squeeze on elective [planned] surgery that will have huge implications for already dire patient waiting times, and this directly relates to the under-funding of previous years.”

• This article was amended on 3 March 2020 to more accurately express remarks by an NHS trust boss on the impact on the NHS if the number of people who contract Covid-19 need medical intervention.