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Tonbridge and Malling Borough Council has become the first local authority locally to cancel council meetings.
The borough said it was cancelling all council and committee meetings until further notice.
It was also requesting the public not to visit council offices unless absolutely essential and instead to carry out all transactions online or by phone or email.
Other group events and meetings, including a Mother’s Day tea scheduled for this Sunday at Tonbridge Castle, have also been cancelled.
A spokesman said: "While the delivery of our services is continuing largely as normal, we are advising that where possible any residents who need to pay bills, renew licences or get advice should avoid travelling to our offices and instead access services via our website, email or telephone.
"Our priority is to support efforts to control the spread of coronavirus and maintain delivery of our core services.
"We have robust emergency plans in place and have set up a dedicated web page to promote the latest health advice from the NHS and Public Health England and also to provide details of any changes to the delivery of council services."