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.
Theresa May is expected to brief her cabinet today on proposals to avoid a hard border in Ireland through a UK-wide customs arrangement that would eliminate most checks on goods. To ease Conservative fears that the United Kingdom could effectively stay in the EU customs union indefinitely, preventing trade deals with other countries, Downing Street is pushing for a review mechanism that would allow the United Kingdom to exit the arrangement.
The Prime Minister said any agreement will be dependent on an "acceptable" framework for future relations in areas like trade and security, expected to be covered in a separate political declaration.
The crunch meeting comes amid mounting pressure to finalise the withdrawal agreement in order to announce the leaving terms at a special summit in November.
The EU's chief negotiator Michel Barnier stressed the United Kingdom would have to come up with a proposal that satisfied its 27 nations that its single market would not be undermined and that there was a guarantee of no hard border in Ireland.
"While the United Kingdom should aim to conclude the Withdrawal Agreement as soon as possible, this would not be done at any cost".
In response, Sir Jeffrey said Dublin's stance was making a no-deal Brexit likely.
The meeting of senior ministers today comes after Justice Secretary David Gauke said a no-deal European Union exit would be "very bad" for the United Kingdom economy.
But the spokesman cautioned: "Don't be under any illusion, there remains a significant amount of work to do".
In a phone conversation with the Irish taoiseach on Monday, Prime Minister Theresa May said any agreement would have to include a review mechanism to bring an end to the backstop.
But it is clear that there are advanced discussions about how to get the deal through Parliament and convince the public if, and when, it is done.
He tweeted: "Such an outcome will have serious consequences for economy of Irish Republic".
Mrs May is understood to view the mechanism as a means of allaying the concerns of Conservative and DUP MPs who want guarantees that any future membership of a customs union is temporary.
Former foreign secretary Boris Johnson has denounced a mooted Brexit deal with the European Union as an "absolute stinker" and urged MPs to reject it.
Looks like we're heading for no deal. "Given that neither was on the ballot in 2016, we believe the ultimate choice should be handed back to the public with a People's Vote".