He has also urged Conservative pro-Remain MPs to "change the course of Brexit" and vote accordingly on a series of upcoming crunch votes in the lower house of parliament.
In what is likely to be a highly-charged appearance before the backbench 1922 Committee on Monday, the Prime Minister is expected to say that the way MPs vote will send a message.
Asked if it was possible for the United Kingdom to remain in a customs union with the EU having left the EU, Mr Brown replied: "I think it is, but I think the issue that we've got to resolve is Northern Ireland".
"But if the Lords amendments are allowed to stand, that negotiating position will be undermined".
One of the key points of difference between the Prime Minister and the rebels is a Lords amendment which states the Government must seek to negotiate a customs union with the EU.
"But the message we send to the country through our votes this week is important".
"We all hang together or we will hang separately", Buckland added, in a plea for unity.
The speech will come on the eve of two days of debates and voting on amendments to the EU Withdrawal Bill, which is scheduled to last 12 hours.
It is expected that Tuesday will see MPs decide whether Parliament should have the power to set the Government's negotiating goals if Theresa May's deal with Brussels is voted down.
Pro-Remain Tories are considering whether to vote in favour of peers' changes to the bill on their demands for the government to stay open to negotiating a customs union with the EU, and on a call for a beefed-up "meaningful vote" for parliament on the final Brexit deal.
Conservative MP Sarah Wollaston said on Monday morning she was "minded" to defy party orders and back the meaningful vote amendment.
Labour and Conservative MPs are bitterly split over Prime Minister Theresa May's desire to keep Britain in the European Economic Area.
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