Prime Minister Theresa May's chief disciplinarian says the government should have told people they would have to accept a softer form of exiting the European Union after May lost her majority in the 2017 general election.

Chief Whip Julian Smith, whose job is to ensure Conservative Party lawmakers vote for the government, makes the comments in a BBC documentary to be broadcast Monday.

Smith says May called the election to strengthen her hand in delivering Brexit, but was weakened when she lost her majority. He says the government "should have just been clearer the consequences of that, the parliamentary arithmetic, would mean that this would be inevitably a kind of softer type of Brexit."

The comments come after Parliament rejected May's EU withdrawal deal for a third time on Friday.