He added the idea of leaving part of the U.K.in the single market or customs union, "is emphatically not something the U.K.is considering".
He had savaged Theresa May's performance in Brussels when she failed to secure agreement over the UK's Brexit divorce agreement.
But Brexit Secretary David Davis said Labour's policy on the customs union and single market had changed "10 times" in the previous year.
The Brexit Secretary was responding to an urgent question raised by his Labour counterpart Keir Starmer.
There is little possibility of a fresh agreement over the border because Theresa May has taken two conflicting stances, in that she has said she does not want a hard border in Ireland but also that the United Kingdom will leave the customs union and single market.
He said that the price of the government's Brexit agreement could be opening up "bitter divides in Ireland".
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Mr Davis pointed to comments made by members of the shadow cabinet on remaining in the single market and customs union, and said: "So much for Labour policy on this matter, we can see why it's changed 10 times in the course of the a year ago".
Mr Davis said the Government was in the middle of an "ongoing round", and that, while progress had been made, a final conclusion had not yet been reached.
"There is much common understanding, and both sides agree that we must move forward together".
Labour's Brexit spokesman, Sir Keir Starmer, last night defended his party's position on Brexit, claiming that it had to "challenge" the Government to see that the negotiations were successful.
Referring to the falling out with the DUP, Starmer joked: "It's one thing to go to Brussels and fall out with those on the other side of the negotiating table, it's another thing to fall out with those supposedly on your own side".
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