"Don't be under any illusion, there remains a significant amount of work to do", the spokesman told reporters.
There is a growing confidence in Whitehall the European Union will accept an all-UK backstop, which would mean the whole of Britain remaining in a customs arrangement with Brussels to avoid a hard Border if a trade deal can not be finalised by December 2020.
The backstop arrangement would come into force should a future EU-UK trade relationship fail to avert a hard border between Northern Ireland and the Republic of Ireland.
The report claims an "all-UK customs deal" will be written into the legally binding withdrawal agreement, which would do away with the need for the controversial "backstop" arrangement agreed by the United Kingdom last December, which would see Northern Ireland remain in full alignment with the EU's single market and customs union rules in the event of a no-deal Brexit.
Speaking at the Great Catholic Conferences in Brussels, Mr Barnier stressed that Britain will remain "in all likelihood" a "neighbour, partner and ally" after March 2019.
The Brexit secretary Dominic Raab had initially wanted the United Kingdom to be able to leave the backstop unilaterally, but both Mrs May and the Irish Foreign Minister rejected this. The agreement would "not be done at any cost", her official spokesman said.
Sterling fell after a senior member of the Northern Irish party which props up May's government said the United Kingdom looked likely to leave the European Union without a deal.
At a Brussels summit in October, EU leaders ruled there was not enough progress in Brexit negotiations in order to call an emergency summit this month to finalise a deal.
The Brexit figurehead was responding to reports that Prime Minister Theresa May is close to striking a deal with Brussels which would allow the creation of a whole-UK customs union, avoiding the need for the Northern Ireland border "backstop" that has been at the heart of the impasse in negotiations.
Later, he even adapted May's "Brexit means Brexit" catchphrase to stress that a "backstop" deal for Northern Ireland was crucial.
A senior DUP figure has warned that the United Kingdom is hurtling towards a no deal Brexit, pinning the blame on the Irish Republic for its hard-line stance on the backstop.
"Can't understand why Irish Government seems so intent on this course".
A no-deal outcome, he said, "will have serious consequences for economy of Irish Republic".
Britons wanting to take their pooches or other beloved pets with them face a slew of new checks if there is a no deal Brexit.