Former cabinet secretary Lord Butler of Brockwell said he backs an amendment calling for the public to be consulted again on the Government's final Brexit deal.
Lord Butler's comments came as the Lords debated the European Union (Notification of Withdrawal) Bill for the second day.
Lord Butler said that while he accepts Britain is leaving the single market to regain control of immigration, a final deal should be put to the people.
Lord Butler said: "Is the outcome of last June's referendum to be interpreted as meaning that a majority of the United Kingdom want to leave the EU whatever the terms? The Government clearly thinks so.
"But on a matter of this importance has not the Government a duty to be sure before our departure becomes final?
"My lords, one has to ask why those who base their arguments for Brexit on the will of the people are now opposed to consulting the people on the outcome of the negotiations.
"One has to suspect that they fear that they will get a different answer. If so, we ought to know."
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