When asked how long it would be before the virus could cause school closures and the cancellation of events such as football matches, Mr Hancock said "in this very early stage there are several weeks before this [infection] becomes very widespread".
He added: "Right now the advice is not to cancel big events, that's the clear scientific advice, it doesn't have any impact now.
"We're not ruling out doing that later."
He said the advice was the same with school closures, unless there is a positive case of somebody in that establishment, "then schools should not be closing".
Despite saying on Sunday it was now "inevitable" that the deadly virus would “become endemic” in the UK, the Health Secretary did not say any extra emergency funding had been set aside to help the NHS.
He said "it really isn't about the funding" but added how the government would be "open" to providing the service with more cash in the future if necessary.
"This is a problem that I think is likely to become more significant for this country in the next days and weeks and therefore we have been making every possible preparation for that," Mr Johnson said, after chairing an emergency Cobra meeting.
He added: "We are in a position to take the steps that will be reasonable to contain the spread of the disease as far as we can and also to protect our most vulnerable."
The comments of the two MPs followed a Cobra meeting, aimed at containing the outbreak, held shortly before four more people in England had been confirmed as having the disease - raising the total to 39 in the UK.
All of them had recently travelled to Italy, a growing hot spot in Europe.
ITV News Political Editor Robert Peston on measures the government may use to tackle the virus
On Tuesday the government will publish its "action plan" on how it will tackle coronavirus, with the number of cases in the UK growing almost daily.
But Mr Hancock said the action plan's implementation will not depend on how many people in the UK have the virus.
"There isn't a precise number that leads to the switch", he said, "because a lot of it depends on what happens in other countries as well".
"We don't have an exact figure, but that isn't because we're holding that back, it's because the scientific judgement on when we move from trying to contain this virus into trying to delay and mitigate its onset here, that decision will be a scientific judgement based in part on the decisions of others around the world," he added.
The Prime Minister said: "It is still the case that the single most useful thing that we can all do to support our NHS to stop the spread of coronavirus is to wash our hands."
He added it is "very important" that people consider that they should "go about business as usual".
It comes as European Commission President Ursula von der Leyen said the EU had raised its risk level from "moderate" to "high", while a senior Public Health England (PHE) official warned of "more widespread infection".
Several cities in Italy remain in lockdown, after 1,694 cases and 52 deaths.
In France, more than a hundred cases have been confirmed, the Louvre Museum remains closed and the Government has banned indoor events with more than 5,000 people.
Nicola Sturgeon said the Scottish Government is expecting a "significant outbreak of coronavirus" after the first case was diagnosed in the country on Sunday night.
Giving a statement alongside Scotland's Chief Medical Officer Dr Catherine Calderwood and the Health Secretary Jeane Freeman, the First Minister said further cases are expected in the days to come.
She said the Government is "planning for the likelihood of a significant outbreak of coronavirus".
The patient who was diagnosed with the Covid-19 virus is "not seriously ill at this stage", Ms Sturgeon revealed.
Meanwhile, shadow health secretary Jon Ashworth urged the government to support those self-isolating over coronavirus.
He said: "Lots of people will be on statutory sick pay and people will be faced with making a choice between putting their health first by isolating, or financial hardship.
"So I hope the government can step in and support those members of staff, those workers out there."
The Cobra meeting was attended by senior ministers as well as chief medical officer Professor Chris Whitty and chief scientific adviser Sir Patrick Vallance, as they ratify the Government’s proposed countermeasures.
Emergency powers set to be unveiled this week to help combat the virus include suspending rules about the maximum numbers of children that a single teacher can be responsible for.
The temporary measures will also allow for emergency medical registrations to create a “Dad’s Army” of retired doctors to back up an already under-strain NHS.