The three drivers have left Hull City Council after finding work elsewhere due to the desperate need for haulage drivers.
A Hull City Council spokesperson said one had taken a long distance haulage job after bin lorry drivers elsewhere were offered as much as £53,780 to move.
They added there were also less agency drivers available but the council were able to fill posts also vacated by one leaving due to Brexit and another switching roles internally.
An East Riding Council spokesperson said they were not experiencing driver shortages at the moment as other authorities shed workers, including North Somerset which lost five in two weeks.
East Riding Council’s spokesperson said: “Thanks to our crews, residents haven’t experienced any changes to their bin collections.”
Hull bin lorry drivers earned between £20,493 and £22,627 a year while East Riding ones made £21,748 as of March, around £30,000 less than salaries being offered by some supermarkets.
The comments come following reports 18 councils were struggling to staff bin collections with drivers at the start of this month.
The lack of drivers has largely led to green waste collections being disrupted as councils divert staff to normal rubbish collections.
Three Devon councils have called on Home Secretary Priti Patel to grant temporary visas to EU drivers to fill vacancies.
The lack of staff shows the current estimated shortfall of around 100,000 HGV drivers nationally is being felt in council frontline waste services.
One North Somerset bin lorry driver was reportedly approached at his cab while having lunch to take a haulage job.
The authority has since been forced to halt green waste collections for two weeks while four councils in Surrey have axed them until next year.
The £53,780 offered to drivers by Waitrose is higher than typical salaries for secondary school teachers, solicitors and architects.
Salaries for Tesco and Iceland drivers have risen by a quarter, with both supermarkets offering joining bonuses of £1,000 and Marks & Spencer promising £2,000.
The shortfall is due to a combination of the coronavirus pandemic and Brexit, as EU citizens who once manned a large number of lorries in Britain return home.
The shortage of drivers has also affected business supply chains and has been a factor in supermarket shelves emptying in recent weeks.
Hull businesses including a cafe and pub previously said supply chain issues had seen them run out of some products while others were becoming harder to source.
Supermarkets including Tesco have also warned shoppers could face shortages of some goods in the run up to Christmas.