William and Kate visited an NHS 111 call centre in Croydon, south London, in the first royal family public engagement in connection with the Covid-19 pandemic.
William urged the public to listen to expert advice and to carry out social isolation, describing the health service as "the very best of our country and society".
“All of us have a part to play if we’re going to protect the most vulnerable. That means acting on the latest expert advice, staying home if we or those we live with have symptoms, and avoiding non-essential contact to help reduce the spread of the virus," he said.
William and Kate meet NHS staff at a virus crisis centre in south London.
The unannounced visit took place on Thursday, but was kept secret so as to not put any additional pressure on the centre, avoid crowds gathering and not clash with the Queen’s statement to the nation in which she urged the country to “work as one”.
Workers told the couple that the number of calls from the public had quadrupled since the crisis began - and that the 999 service had just had the busiest three days in its history.
Euan Flood, 34, a paramedic, said he was getting calls "one after the other".
"Currently, we have a few hundred calls waiting to be called back, anything from a day to two, three days old," he told the couple.
"We are hearing a lot of panic about self-isolation. People don’t really understand the guidance, so we have to explain it to them fairly regularly. But once we explain it people tend to understand why we are advising it.”
During the visit Kate told the first call handler she spoke to: “It’s amazing. You’re doing such a great job bringing everyone together and providing that, the support system, for the whole public."
The visit saw the couple adhering to the latest protocols about dealing with the disease, with no handshakes, frequent hand-sanitising and a conscious effort to socially distance themselves from people.
Garrett Emmerson, the chief executive of the London Ambulance Service, said the Duke suggested that royal visits might change as the virus progresses through the population.
"We are all learning new ways of behaving socially as a result of this, and indeed new ways of working. We were talking with the duke about potential future visits if we are in further stages of social distancing – we may be doing remote conferencing for events like this," he said.
The duke asked repeatedly whether members of the public could help by volunteering, with Mr Emmerson replying the NHS was "looking at that."
"We have a lot of former employees, retired employees, people who used to work in our service but are now in other fields, for instance the airline industry" he said.
“As staff are laid off, they are saying, ‘Can we bring our skills back?"
William himself used to work as an air ambulance helicopter pilot, and Mr Emmerson was later asked if he could bring his skills to the ambulance service.
“As he knows well, we have an air ambulance service here in London. I know that he would be welcome there any time," he answered.
William, 37, is the most senior royal in the line of succession who is young enough not to be affected by warnings that over 70s are more at risk of serious complications from the Covid-19 illness.
William, whose two eldest children Prince George and Princess Charlotte are affected by school closures, launched a video appeal on Wednesday for the National Emergencies Trust to raise money on behalf of local charities working with those most at risk during the crisis, .
Before he left the call centre, he told the staff: “Well done on you guys. It’s lovely to see you."