The Labour leader said the haulage industry was “beyond frustrated” at the lack of a clear plan by ministers to alleviate the problems as filling stations ran dry.
“The Government has reduced the country to chaos as we track from crisis to crisis and the Government is not gripping this,” Sir Keir told BBC News in Brighton, where Labour is holding its annual party conference.
“I spoke to the haulage sector this morning, to the businesses that are absolutely in the middle of this, and they are beyond frustrated.
“They said it’s a Government that is denying there’s a problem, then blaming somebody else, and then coming up with a half-baked plan.”
He said there were doubts among the industry that the Government’s plan to issue 5,000 three-month visas to foreign lorry drivers to make up for the shortage of truckers would work to help the issues.
Sir Keir said there was a “strong view” that they would need to be for at least six months if they were to tempt sufficient numbers to come to the UK.
“The Prime Minister should take that action today, prioritise key workers and start issuing enough visas and for long enough,” he said.
“The strong view this morning was that three months visas won’t work, they’ve got to be six months visas.
“But this problem was predictable and predicted and the Government has absolutely failed to plan.”
Sir Keir resisted blaming Brexit directly for the shortage of HGV drivers but accepted it was partly a consequence of leaving the European Union.
Speaking to Channel 5 News, he said: “I wouldn’t say that Brexit is to blame. What I would say is that it was inevitable as we exited the EU that we needed a plan to deal with drivers.
“That is obvious whether you voted Remain or voted Leave, and we took that decision years ago.
“And here we are with a shortage of drivers which was completely predictable and predicted – and the Government hasn’t got a plan.”
Speaking later to Sky News, Sir Keir said: “What is the sole cause of this problem? The Government has known for some time that there are consequences of us leaving the EU, one of which is lorry drivers.”