The campaign will feature radio and social media broadcasts and will aim to “further raise awareness” about the potential impacts.
The government is set to launch a publicity drive to prepare the public for the possibility of a “no-deal” Brexit.
Whitehall departments and the health regulator will release guidance on how members of the public can handle any potential issues that may be caused by such an outcome.
The campaign will feature broadcasts on radio and social media – and comes after ministers published information advising businesses on how best to prepare for no deal.
Writing in the Daily Express, Brexit Secretary Stephen Barclay said that scenario would be “far more likely” if MPs reject Theresa May’s agreement when it is put to vote later this month.
“The pace and intensity of the work we are doing reflects the potential scale of this disruption to people and businesses across the UK that a no-deal scenario could bring,” he wrote. “The Home Office will next week be publicising guidance on new passport rules for people travelling to many European countries. These rules would mean some people have to renew their passport earlier than planned.”
Mr Barclay said the Home Office would publicise advice, already available online, on how to renew a passport.
He added: “On Tuesday, we will start a new phase in our public information campaign, using radio and social media to further raise awareness.”
The move drew criticism, with Labour MP Virendra Sharma, a supporter of the second referendum, saying: “It’s a bleak start to 2019”.
He said: “The government has already spent hundreds of thousands pushing its Brexit agenda on social media. Now it wants to spend more taxpayer’s money distracting from the gaping flaws in its own deal by warning of a no deal catastrophe.
On Thursday, Mr Barclay will convene a meeting of ministers to discuss the latest no-deal preparations.
As she battles to get her deal through parliament, Mrs May spoke with German Chancellor Angela Merkel on Wednesday.
A Downing Street source said the PM is due to hold talks with other EU leaders in the coming days, in a bid to “get the assurances MPs need” on the Irish border backstop.
Brussels has confirmed “no further meetings are foreseen” as the negotiations have “concluded”.
A spokesperson for European Commission President Jean-Claude Juncker said the leaders of the remaining 27 EU nations “have been very clear that it will not be renegotiated what is on the table”.
Irish Prime Minister Leo Varadkar spoke with Mrs Merkel on Thursday and said both leaders “stand by” the withdrawal agreement.
“We’re happy to offer reassurances and guarantees to the UK, but not reassurances and guarantees that contradict or change what was agreed back in November,” he said.
Meanwhile, Northern Ireland’s Democratic Unionist Party has confirmed it is still opposed to Mrs May’s deal.
Speaking after a meeting with the PM in Downing Street, deputy leader Nigel Dodds said: “The withdrawal agreement, as currently proposed, flies in the face of the Government’s commitments on Northern Ireland as we leave the EU.”
Opposition to the Irish border backstop caused Mrs May to postpone the vote on her deal, originally due in December, until after Christmas.
It is now scheduled to take place in the week beginning 14 January, but former Brexit secretary David Davis has suggested it could be delayed again.
Meanwhile, dredging has begun at the Port of Ramsgate as preparations continue to get the port ready for the possibility of no deal.
Seaborne Freight, which recently received a much-criticised £13.8m government contract, is paying a Dutch dredging company to do the work.