Neil Findlay hit out at Tory hardline Brexiteers in the European Research Group - chaired by MP Jacob Rees-Mogg - as he slammed the Conservative Government’s approach to Brexit.
He insisted Labour had “tried to bring some common sense” to the Brexit process.
Mr Findlay, speaking at the Scottish Labour Conference in Dundee, said: “With that deadline looming our businesses have no idea how data will be transferred between the UK and the EU.
“They have no idea how goods will be transported, no idea what customs arrangements will be, no idea what travel arrangements will be in place, whether flights will take off and land, whether ferries will sail and be docked.
“What an absolute shambles it is.”
The Prime Minister is “at the mercy of the eejits, rogues and galoots of the ERG, as they are better known,” he added.
Mr Findlay added: “We’ve got the stockpiling of medicines, the stockpiling of food and a ferry contract awarded to a company that didn’t have any boats.
“I know that Laurel and Hardy have made a comeback this year but I was unaware it was in the shape of (Health Secretary) Matt Hancock and (Transport Secretary) Chris Grayling.”
The Labour MSP hit out at the “rotten, divisive, arrogant, incompetent, elite Tory Government” who he said were responsible for “this fiasco”.
And he insisted a second Brexit referendum was needed to end the “paralysis” in the House of Commons, saying that at the moment there was “a political stalemate that shows no sign of ending”.
With Mrs May facing key votes in the Parliament in the coming days, Mr Findlay said: “This week, no-deal must be taken off the table once and for all, and we should see the extension of article 50 to prevent a lemming-like dive off the cliff edge.
“If Parliament remains in deadlock then, in an attempt to break that deadlock, we have to take it back to the people.”