Furious residents have demanded action after mounting refuse on three roads was not collected for a month.
But Bradford Council blames indiscriminate parking blocking the path for refuse vehicles - and yesterday swept in to clean up the area as a one-off.
Residents and councillors in Great Horton had asked for an explanation as to why the weekly collection was not completed.
In blaming inconsiderate motorists, the Council urged owners to keep the route clear on collection days.
Councillor Sajawal Hussain (City, Lab), said the build-up of bin-bags and domestic waste had led to an increase in the number of rats in the area.
He said: "They said they would come and clean it up, but they have not given us an explanation why it has been left so long. Because of the rubbish, it has encouraged the rats and mice to come out, as they have constant access to the refuse.
"This happens quite often in my ward - you hardly miss a week where there is no complaints on refuse collection from City ward.
"I have been told the refuse collectors do sometimes come and just went by. But four weeks is too long to leave the streets like this."
The backstreets of Oulton Terrace, Rothesay Terrace and part of Great Horton Road have all been affected.
Tasvir Hussain, 46, a resident of Oulton Terrace, said the full bins left an unpleasant smell.
He said: "We have seen quite a lot of rats and even foxes as well - it does not look or smell nice at all because there is too much rubbish.
"I just want to see it clean, it gives the area a bad name.
"My children play out here all the time and I am often concerned for their health and safety when they play just outside our house - that is not right."
Sajid Khan, 21, also of Oulton Terrace, said there should be no excuses for not taking rubbish away.
He said: "It is not acceptable. We get rats the size of cats and dogs round here.
"At the end of the day, that is their job, but they do not seem to be able to do that, so what are they getting paid for? I think an excuse they give is that parked cars are in the way, but this road is used as a through-way, so people can get in and out easily enough.
"If there was someone in the way, they should ask and that person would move their car."
Ian Bairstow, head of the waste and street scene service at Bradford Council, said: "There have been one or two occasions recently when we have not been able to do our usual refuse collections from these areas because of inconsiderate drivers blocking access to properties.
"However, we will continue to visit these properties on a weekly basis on the normal day of collection and we would request that the owners move their vehicles.
"We have already done a special collection yesterday from Oulten Terrace and Rothesay Terrace and will return to the other addresses as soon as we are able."
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