Tonbridge and Malling Borough Council asked its residents not to put out green-lidded recycling bins and green boxes to allow crews to catch up with a backlog of missed collections.
The council said that “like many other waste service providers, the council's contractor, Urbaser, has been struggling with a shortage of drivers in recent months”.
The council said it expects full service to be resumed from Monday 12 July.
According to the Road Haulage Association (RHA), there is a national shortage of HGV drivers in the UK of between 85,000 and 100,000.
The shortage is thought to be a result of a combination of Covid-19 and Brexit.
The large majority of truck drivers in recent years have been Eastern European. The RHA estimates that prior to the pandemic, there was a shortage of truck drivers in excess of 60,000.
It said Covid-19 had exacerbated this, with many drivers having returned to their country of origin during extended periods of lockdown and restricted travel. “The vast majority have not yet returned,” it said.
The RHA said the uncertainty of Brexit and future rights to live and work in the UK had also dissuaded many drivers from returning.
The group said the shortage was now “at crisis point”.
Other councils are also seeing disruption to waste services including the borough of Sutton in South London and Arun District Council in West Sussex, which has said it will try “to get services back on track as soon as possible”.
Meanwhile Tesco, the UK’s biggest food retailer, has said the driver shortages were creating 48 tonnes of food waste each week, the equivalent of two truckloads.