"I'm confident that people will be able to get their toys for Christmas," Dowden, who is also the co-chairman of the ruling Conservative Party, told Sky News broadcaster.
Comments from the minister without portfolio in the Cabinet Office came as authorities at Felixstowe, a port on the east coast of England, confirmed in a statement that the pre-Christmas peak, combined with hauling shortages, congested inland terminals, poor vessel scheduling, and the pandemic, have resulted in a build-up of containers at the port.
The Danish shipping company Maersk Line also said it is re-routing its vessels to other ports in Europe due to the backlog.
Dowden said the government is working through these challenges but claimed they are not exclusive to the UK, as other European countries, the US and China also have a shortage of drivers.
"This is why we have been taking steps to address it, whether it is, for example, with training, 5,000 more places for training HGV [Heavy Goods Vehicles] drivers, making the process more flexible," he said.
The British government blamed the shortage on the suspension of 40,000 trucker training tests during the COVID-19 pandemic, but the Road Haulage Association claimed that around 20,000 foreign drivers left the country after Brexit put an end to the free movement of people between the European Union and the UK.
The lack of truck drivers along the supply chain has already translated to shortages of fuel and food products at gas stations and supermarkets.