The government says it plans to help councils in England bring back weekly bin collections as many continue to deal with a huge backlog of rubbish.
Some areas, including Birmingham and Exeter, have not had a collection for four weeks.
Local Government Minister Bob Neill said he wanted to "reverse the legacy of Labour's savage cutbacks to weekly rubbish collections".
Councils say they are working hard to clear the backlog.
They have blamed severe winter weather, and in particular icy roads, for preventing normal collections for several weeks.
The problem has been exacerbated by the festive break and the increased amount of waste produced by households over Christmas and New Year.
There are concerns the situation could encourage rats and cause other health hazards.
'Not a major problem'
Council staff in some areas have worked extra shifts over the weekend and on bank holiday Monday, and casual workers have been called in to help.
But the leader of Labour-led council Exeter told the BBC on Tuesday he did not believe it was necessary for refuse collectors to work on Christmas bank holidays.
With regard to fears over rubbish piling up in the street, Pete Edwards added: "I do not see it as a major problem."
Mr Neill said Mr Edwards' comments were "irresponsible and insensitive" and he should apologise.
"This sort of complacency became the norm under the last government, with Labour doubling council tax whilst slashing weekly rubbish collections," he said.
"We need to start treating residents as the customer and putting them back in charge.
"We will be setting out measures in the coming months to help councils reverse the legacy of Labour's savage cutbacks to weekly rubbish collections."
Under the previous government, councils were encouraged to save money with fortnightly collections and were threatened with being marked down by the Audit Commission - which monitors council spending - if they ignored that guidance.
A spokesman for the Department of Communities and Local Government said it would not force councils to reinstate weekly collection, but had scrapped the Audit Commission and removed all the incentives to cut services.
Problems have been reported across the UK, with Birmingham, north London and parts of Merseyside among the worst affected.
BBC News website readers have expressed their concern.
Pam Gurney, from Exwick, in Exeter, said: "Our last black bin collection was made on December 6th. The amount of rubbish is disgusting and I am horrified to hear the councillor say that there is not a problem."
Sarah Turner, from Wallasey, Merseyside said: "The bins in my street have not been emptied now for weeks.
"My rubbish is in a small mountain outside our house. I have two young children, one aged 20 months and the other three, both still in nappies. It's a health hazard."
The Taxpayers' Alliance, a pressure group which wants to see lower taxes, accused councils of "a massive failure".
"This is exactly the type of service that taxpayers expect to see performed properly and regularly," campaign manager Charlotte Linacre said.
"Council tax has nearly doubled in the last 10 years so taxpayers are shocked when local governments seem incapable of providing basic services."
Working to rule
In Birmingham, the city council apologised for the disruption and promised to have the backlog cleared by Friday.
But the situation has been made worse by industrial action, which led to binmen walking out on 20 December in a pay dispute and subsequently working to rule.
Now staff have voted to take two further half-days of strike action in mid-January as part of a dispute over equal pay for male and female staff.
A Local Government Association spokesman said the exceptional weather had been the major factor hitting councils.
"They have done a terrific job trying to keep up the service and are working extremely hard to clear any backlogs," he added.