Yorkshire-based Paynes Dairies has been forced to halt up to 10 per cent of its orders thanks to a delivery driver shortfall.
Managing director Charles Payne said the company, which made £92 million in sales last year, had been “quite considerably” affected.
It comes as Arla, the UK’s largest dairy supplier, warned that supermarkets faced a “summer of disruption” to milk deliveries.
“It’s not a good situation, and the government’s increase of driver hours by an hour a day hasn’t helped,” Payne told The Grocer.
Last month, ministers controversially raised the daily limit for time behind the wheel from nine to 10 hours.
Two 11-hour stints per week have also been allowed.
Instead, Payne called on the government to tempt European drivers back to the UK by relaxing visa rules, and encourage retirees to return to work.
“Until that happens, this problem won’t go away,” he warned.
Dairy UK chief executive Judith Bryans said the situation was particularly difficult for the industry.
“The food sector in general needs the government to give skilled worker visas to drivers, but given that we have fresh products in dairy we really need that to happen sooner rather than later,” she said.
Earlier this week, Arla announced that driver shortfalls had forced it to cancel 25 per cent of its retail orders.
“We are asking for the industry and government to work together to recognise we are in a crisis and address the issue,” managing director Ash Amirahmadi said.
The supplier hopes to plug the shortage with a £2000 bonus for new recruits.
Supermarkets including Tesco and Waitrose are also offering four-digit rewards in a bid to attract drivers.