Boris Johnson, who is self-isolating after testing positive for Covid-19, says stricter restrictions could be put in place if necessary.
Britons will also get a leaflet detailing government rules on leaving the house and health information.
It follows criticism over the clarity of government advice to date.
The number of people who have died with coronavirus in the UK has now reached 1,019, with a further 260 deaths announced on Saturday.
There are now 17,089 confirmed cases in the UK.
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.