It follows criticism over the clarity of government advice to date.
In the letter being sent to 30 million households at an anticipated cost of £5.8m, Mr Johnson writes: “From the start, we have sought to put in the right measures at the right time.
“We will not hesitate to go further if that is what the scientific and medical advice tells us we must do.”
Tough measures to tackle the spread of coronavirus, including a ban on public gatherings of more than two people and the closure of shops selling non-essential goods, were introduced last week, reports BBC.
The number of people who have died with coronavirus in the UK has now reached 1,019 till Sunday, worldometer reported.There are now 17,089 confirmed cases in the UK.