Everyone should worry about no deal, the civil servant who was, until March, head of the Brexit department has said.
Philip Rycroft, who resigned after 18 months, told the BBC's Panorama no deal was "fraught with risk".
And NI police said no deal could help recruitment for paramilitary groups.
Both the candidates in the race to replace Theresa May as prime minister - Jeremy Hunt and Boris Johnson - have said they would be prepared to leave the EU without a deal.
Former Defence Secretary Sir Michael Fallon said there was "no reason at all" why new negotiations with the EU could not be completed in "the next three months".
But the EU has repeatedly refused to re-open negotiations.
The UK had been due to leave the EU on 29 March but this date was delayed after MPs repeatedly rejected Mrs May's deal. Currently, Brexit is set to take place on 31 October.
In a no-deal scenario, the UK would immediately leave the EU with no agreement about the "divorce" process, immediately coming out of the single market and customs union and institutions like law enforcement body Europol.
Those against say it would damage the economy, especially industries like farming, and cause widespread disruption, but some politicians insist problems could be quickly overcome.
The government says it has been preparing for almost three years to minimise that disruption and to provide people and businesses with information they need to get ready.
What is a no-deal Brexit?
- The UK would leave the single market and customs union - arrangements designed to help trade between EU members
- Checks at UK-EU borders could cause bottlenecks at ports
- No deal also means immediately leaving EU institutions, such as the European Court of Justice
- Many politicians and businesses say no deal would damage the economy. Others say the risks are exaggerated
In his first broadcast interview since stepping down as permanent secretary at the Brexit department, Mr Rycroft said the planning operation for exiting the EU was "an unprecedented situation" and "the biggest exercise across government over the last few decades".
He told Panorama: "This has been an extraordinary exercise to which the civil service is responding brilliantly well… The planning I think is in good shape, absolutely… but of course what that doesn't mean is that there won't be an impact from Brexit, and particularly a no-deal Brexit, because that is a very major change and it would be a very abrupt change to our major trading relationship."
"The rational outcome over the next few months is to get a deal because that is overwhelmingly in the economic interest of both the EU and the UK."
Mr Rycroft continued: "It's not in the UK's interest to have no deal, it's not in the EU's interest to have a no deal.
"I think everybody should be worried about what happens in a no-deal situation. We would be taking a step into the unknown."
But Sir Michael told BBC Radio 4's Today programme said no deal was the "ultimate fall back" and needed to be prepared for "so that our partners are convinced that this is a deadly serious negotiation".
"We have got three months to do this with a fresh approach," he said. "We need some alternative arrangements for Northern Ireland - some of that technology is already in place - we need the right to exit the backstop if the negotiations fail, we need some improvements to the political declaration.
"These aren't the biggest things, but what they do require is some optimism and ambition and above all some energy.
"We will have a fresh team, a fresh prime minister and there is no reason at all why this can't be done in the next three months."
In the event of a no-deal Brexit, additional checks on goods being delivered across the UK-EU border could result in delays on the roads - especially around the Port of Dover in Kent, which handles 17% of the UK's goods trade.
Richard Burnett, chief executive of the Road Haulage Association, said working with the government to prepare for no deal had been "a frustrating process". He said: "We have no clarity of the processes - what's actually going to happen on day one."
Mr Burnett told Panorama that Transport Secretary Chris Grayling had left him a voicemail expressing his disappointment after the RHA issued a press release following a private briefing.
In response, Mr Grayling said the haulage industry had been heavily involved in EU preparatory work and would continue to be so.
"It is obviously disappointing when someone issues a press release on the back of what was a private working group to discuss how we best approach both a deal and a no deal," he told the BBC. "But we have continued to meet and engage with them."
The Police Service of Northern Ireland also told the BBC of its concern at the impact on security of a no-deal Brexit.
There are fears that one could lead to the introduction of a hard border between Northern Ireland and the Republic of Ireland - a situation Sinn Fein has said would lead to further calls for a referendum on Irish unification.
PSNI Assistant Chief Constable Tim Mairs told Panorama: "We know that the New IRA and other groups continue to recruit people and we believe that Brexit provides an opportunity for them to encourage people to recruit."
But he added that, despite their worries, to date the PSNI had not seen "any upsurge" in violence or recruitment being driven by Brexit.
Mr Mairs also expressed fears price differences on the border could create "new opportunities" for criminal gangs, claiming: "We would see, traditionally, connections between some of those groups and more violent groups.
"The potential impact of a no deal on the economy in Northern Ireland is significant, and that would, in our view, present potentially significant security concerns."
Will a no-deal Brexit happen?
The handling of Brexit has been the key issue in the Conservative leadership race.
Frontrunner Mr Johnson has said the UK should prepare "confidently and seriously" for a no-deal Brexit, but believes the chances of it happening are "one million to one against".
He has said he will try to get a new deal negotiated with the EU, but has promised to leave the EU with or without one on 31 October.
His rival, Mr Hunt, also wants to change the withdrawal agreement negotiated by Mrs May and thinks this can be achieved by the end of October.
He has said he is prepared to delay Brexit beyond that date, if there is a prospect of getting a deal. If not, he would be prepared to leave without one but with "a heavy heart".
Meanwhile MPs opposed to no deal are seeking ways to block such an outcome. Tory MP and ex-minister Sam Gyimah says there are "30 plus" Conservative MPs who would vote to block a no-deal Brexit.
- Panorama's No-Deal Brexit: Are We Ready? will be broadcast at 20:30 BST on BBC One.