Refuse workers in Birmingham have voted to reject a “totally inadequate” offer from the city council aimed at ending a long-running strike over pay, union Unite said.

The action, which began on March 11, has seen thousands of tonnes of rubbish go uncollected and warnings issued of a public health emergency.

Unite said the deal would have included “substantial” pay cuts for workers and did not address potential pay cuts for 200 drivers.

Unite general secretary Sharon Graham said: “For weeks, these workers have faced attacks from government and their employer pushing the lie that only a handful of workers are affected by the council’s plans to cut pay by up to £8,000.

“Instead of peddling untruths about these low paid workers and focusing on winning a media war, the government should have taken the time to check facts and used its office to bring the council to the table in a meaningful way.

“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.”

Army logistics are helping to tackle the rubbish piling up on Birmingham’s streets but there are “no boots on the ground”, Angela Rayner has said.

Speaking from Scunthorpe, the Deputy Prime Minister said: “There’s no boots on the ground, let me be very clear, we’ve deployed a couple of army logistics to help with the logistical operation of clearing up the rubbish.

“We’ve got over two-thirds of the rubbish cleared off the streets now, this week we’ll start to see cleaning up the pavements and streets as well as the clearance of all of that rubbish, I’m very pleased about that. The kids are off school, obviously it’s Easter holidays, we want that rubbish cleared.”

Asked if taxpayers would have to foot the bill, Ms Rayner said “this all stems from equal pay liabilities”, adding: “We’ll continue to work with the council to bring down the costs and the liabilities they had with equal pay, which is part of this process, and make sure that the workers are treated fairly as part of that process.”

Military personnel helping Birmingham City Council with its response to the city’s bin strike have “operational planning expertise”, Downing Street has said.

“The residents of Birmingham are our first and foremost priority,” the Prime Minister’s official spokesman said.

“That’s why we’ve provided a number of staff to support the council to help get the streets cleaned up and address the public health risks.

“This includes co-ordinating the local response with local authorities, providing additional vehicles and crews, and opening household waste centres to Birmingham residents and, as set out over the weekend, a handful of office-based military personnel are supporting operational planning and have made themselves available to the council to support.

“And as the Deputy Prime Minister has said, we are now urging Unite to suspend its action and accept the offer that is on the table.”

He said the recruits were “purely office-based military personnel with operational planning expertise”, with “no plans” to bring in front-line personnel to help the authority.

The spokesman added that more than 100 vehicles had left depots on Monday morning, with 12,500 tonnes of waste cleared since April 4.