Andy Street, the Conservative Mayor of the West Midlands, has said he is "frustrated" and "amazed" at the attitude of hardline Brexiteers in his own party.
He said opponents of Theresa May's plan for Brexit - which includes a free trade area for goods - were not basing their arguments on "economic reality".
But the mayor backed the Prime Minister's proposals, saying she had listened to the needs of manufacturers in the West Midlands.
Many employers, including car manufacturers such as Jaguar Land Rover and Nissan, have warned that the UK must retain access to the EU single market and customs union after Brexit.
And speaking to website Politico, Mr Street said he'd found it "difficult" to watch some elements within the Conservative Party dismiss their concerns.
He said: "Some members of my party have said things that I am pretty amazed at. And they're wrong.
"The Conservative Party has always been understanding and supportive of business. So I do find that difficult to understand."
He said he backed Mrs May’s proposals for Brexit, known as the Chequers plan, largely because it promises single market membership for goods.
He said: "That really, really, matters to us."
And he praised the Prime Minister for "facing down" the hardline Brexiteers in the party, Politico reports.
Some have opposed the Chequers plan, arguing that it would mean the UK continues to obey EU rules.
He said: "I get very frustrated with the loud noises that I happen to think are not based on the economic reality day to day."
The West Midlands Mayor did not criticise anyone by name. High profile critics of the Chequers plan have included former Foreign Secretary Boris Johnson.
Mr Street also confirmed in the interview that he plans to run again for the post of West Midlands Mayor when the next election takes place in 2020.
But he did not rule out standing for Parliament in the future, saying only that it was "highly unlikely".