The vote came as army logistics staff were called in to try to ease a crisis now in its sixth week.

The Unite union said its members in Birmingham voted overwhelmingly against what it called a "totally inadequate" offer.

"The rejection of the offer is no surprise as these workers simply cannot afford to take pay cuts of this magnitude to pay the price for bad decision after bad decision," Unite General Secretary Sharon Graham said.

"This dispute is not about a pay rise, it is about preventing serious pay cuts," she said.

Hundreds of workers walked out on March 11, with Unite saying some employees stood to lose pound8,000 ($10,400) a year under a planned restructuring of the refuse service.

Deputy Prime Minister Angela Rayner said two-thirds of the rubbish that had accumulated on the streets had now been removed.

She added that military personnel were helping the Birmingham City Council with the logistics of removing as much rubbish as possible, but that there were "no boots on the ground".

The accumulation of rubbish left to fester on the streets during an unusually warm spring has prompted public health concerns, with residents reporting bags being ripped open by rats, cats and foxes.

Prime Minister Keir Starmer's spokesman said the "purely office-based" military personnel" were helping with "coordinating the local response with local authorities, providing additional vehicles and crews, and opening household waste centres to Birmingham residents".

"We are now urging Unite to suspend its action and accept the offer that is on the table," the spokesman said.

More than 100 vehicles had left depots on Monday morning, with 12,500 tonnes of waste cleared since April 4, he added.