"We agreed today that the conditions for an agreement are not met, due to significant divergences on level playing field, governance and fisheries", the EU's Barnier and UK's Frost said, in a tweeted joint statement.
A top aide in London said Prime Minister Boris Johnson is "optimistic" about striking a deal but ready for Britain to move on without one.
"I'm confident from what I hear that progress, good progress is being made but we're going to do a deal that is right for Britain, if such a deal is available", Williamson told Sky.
"Time is in very short supply. There's no denying that", he told the BBC.
Barnier, Frost and their teams have spent the week locked in talks in a London conference center after a week of late-night sessions fueled by deliveries of sandwiches and pizza.
With less than four weeks left until the United Kingdom finally exits the EU's orbit on Dec 31, both sides are calling on the other to compromise over fishing, state aid, and how to resolve any future disputes.
The two countries needed to wrap up the deal as the existing Japan-EU pact will not cover Britain after the completion of the Brexit transition period in December and could result in impositions of higher tariffs on both countries.
Talks have dragged on as one deadline after another has slipped by.
During a visit to Portsmouth, he said: 'As soon as there's a deal we'll look at it, but if the choice is a deal or No Deal, then a deal is obviously in the national interest'. On Sunday, Britain said the negotiations were in their final week. European Council President Charles Michel said.
It was no different on Thursday when European Union officials said that the remaining differences couldn't be bridged in "a matter of hours" despite swirling excitement that a decisive breakthrough was imminent. "But the end of December is the end of December and we know that after the 31st of December we have the 1st of January, and we know that we need to have clarity as soon as possible".
The French sparked a blow-up in the talks after forcing Mr Barnier to make "eleventh hour" demands that prevented negotiators from getting a deal over the line. That will hurt both sides, but the burden will fall most heavily on Britain, which does nearly half its trade with the EU.
An agreement means "finding a way to get a fair deal for both sides on fisheries, which has proven really, really hard", he said, adding that fair competition and governance were the two other main issues left.
In one of the last-ditch attempts on Thursday, the talks were impeded again when France, along with several other European Union states, expressed concerns over Brussels' readiness to make too many concessions to London. Clement Beaune, France's European affairs minister said he will make a decision on a deal based on how it impacts his country.
"Even with an agreement it will be more complicated".
MPs will vote on the UK Internal Market Bill on Monday, giving ministers the power to break global law by ignoring provisions in the agreement relating to Northern Ireland. There is a lingering lack of trust since the British government introduced legislation that ministers admitted would breach the previous divorce agreement.
Last month the House of Lords inflicted on the Government the largest defeat in more than two decades over the legislation.
"And of course we must also prepare for all scenarios, including for the possibility that there won't be an agreement", he said.