The Duke and Duchess of Cambridge made the remarks in a wide-ranging BBC interview where the royal couple spoke about the pandemic, mental health and the National Health Service (NHS).
Prince William described how the three-week lockdown had been “frustrating” for many people and “pressure, stress and isolation” had been building up.
“If we are going to go forward with more time spent in lockdown, then there is going to be an ever-increasing need for people to look after their mental health and take it seriously and also know where to go to get the support they might need,” he told the BBC.
The Duchess said there had been a focus on physical well-being during the lockdown – with people being told one of the reason they can leave their homes is for one form of exercise a day.
“While that’s hugely important we mustn’t forget our mental well-being as well and making sure you’re reaching out to those people around you that you have access to – even if it’s over the phone or online to really make sure you have those conversations,” she said.
Prince William further said that there was a concern people might think they were “not worthy of support” because of the pressure on services during the coronavirus pandemic.
During the BBC interview, the Duke and Duchess also praised NHS workers and said they were making the nation proud with their “stoicism and determination” to get through the pandemic.
The Duchess also said they had faced “ups and downs” during the lockdown “like lots of families”.
She said homeschooling their children – Prince George, Princess Charlotte and Prince Louis – had been “challenging” but they had a kept a strict regime.
The overall coronavirus death toll in the UK has risen to 13,759 while the number of infections recorded so far has reached 104,148 since the outbreak began.