Mr Smith suggested ministers pursued the wrong strategy after the Conservatives lost their Commons majority in the 2017 snap election, and should have accepted a softer form of Brexit.
A spokesman for the Prime Minister declined to discuss whether she had been warned about his remarks in advance of the broadcast.
“The thing that people forget is that the Conservative Party went to get a majority in order to deliver Brexit [and] failed to get a majority,” Mr Smith said in a BBC documentary broadcast last night. “The government as a whole probably should just have been clearer on the consequences of that. The parliamentary arithmetic would mean that this would be inevitably a softer type of Brexit.”
He said he was “frustrated” by MPs who “don’t see the light as clearly as I do”.
Mrs May’s deal has now been defeated three times in the Commons, with large rebellions by Tory MPs on each occasion.
However, Mr Smith highlighted a lack of discipline extending all the way to the Cabinet, with ministers “sitting around the Cabinet table…trying to destabilise [the Prime Minister]”.
“This is I think the worst example of ill-discipline in Cabinet in British political history,” he said.
Asked at a Westminster media briefing whether Mrs May shared Mr Smith’s assessment of Cabinet ill-discipline, the spokesman replied: “The Prime Minister has said on any number of occasions that this is a subject which brings out strong emotions in MPs on all sides of the debate.”
The spokesman added: “I will leave it to historians to make their judgments on history.”