It came as a poll of 1,000 adults found that one in 10 people would not contact their GP even if they had a lump or a new mole which did not go away after a week, while a third are worried about seeking help during the epidemic.
Forty per cent of those with concerns said they did not want to be a burden on the NHS, while more than a third feared contracting coroanvirus.
Prof Johnson said: “My message is clear: people should seek help as they always would.
“We know that finding cancer early gives us the best chance to cure it, and ignoring potential problems can have serious consequences now or in the future.”
He said online consultations meant patients could be assessed remotely, while a number of “Covid-free cancer hubs” have been set up.
On Tuesday night the head of the London Nightingale hospital said the NHS needed to “radically reorganise itself” in order to provide environments where patients are not at risk of infection.
Senior author Professor Harry Hemingway, director of the UCL Institute of Health Informatics, said: “The overall impact of the Covid-19 emergency on deaths in cancer patients could be substantial.
“There are many factors operating here, including rapid changes to diagnosis and treatment protocols, social distancing measures, changes in people’s behaviour in seeking medical attention and the economic impact of Covid-19, as well as deaths due to Covid-19 infection.”
Dr Alvina Lai, from the UCL Institute of Health Informatics, said: “Our findings demonstrate the serious potential for unintended consequences of the response to the Covid-19 pandemic, which may negatively impact on patients with cancer and other underlying health conditions.
“It is vital that these patients are recognised as being vulnerable and that their care is managed appropriately.”