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Medway Council says household waste will be collected today.
Today's collection had been cancelled due to heavy snow fall being predicted.
Because conditions are not as severe as first thought the council has taken the decision to carry out some collections to clear any backlog although some roads are still inaccesible.
Refuse not collected today will be collected next week.
A spokesman said: "We are sorry for any confusion this may cause residents. "Our refuse teams have been working in difficult and unpredictable circumstances for the last few weeks and are doing their best to clear as much as they can."