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A council leader has pleaded with residents to wear face masks.
Medway's Cllr Alan Jarrett says its vital the community plays its part in attempts to avoid future lockdowns.
From tomorrow, coverings are mandatory in more public places.
As well as shops and public transport, they will also be required in venues and facilities operated by the council. These include libraries, community hubs, heritage sites, children and family hubs, crematorium chapels and the register office.
The top Tory said: "It is absolutely essential we all do our bit to help protect others and ourselves during this terrible pandemic.
"It is also important to protect the staff who work in all these places providing you with products and services that you need and enjoy."
People may be refused entry to premises across Medway if they don't wear masks and do not have an exemption.
He added: "We have seen in recent weeks how easy it is for the virus to take hold again. Local lockdowns have been applied in a number of areas including Leicester, Blackburn with Darwen, Calderdale, Kirklees, Bradford and most recently Aberdeen.
"We want to avoid any such restrictions here in Medway and to pave the way for a successful return to school for our children in September and to keep shops, pubs and restaurants and many other venues open for you.
"Please do also continue to heed the government social distancing advice and keep washing your hands regularly.
"There are, of course, some people who are exempt from wearing a face covering due to an age, health or disability reason so please do be mindful and respectful of them too.
"We all have an important part to play to protect Medway and it has never been more important for everyone to take the necessary steps to reduce the spread of coronavirus. Please do urge your friends and family to do their bit too.
"We must avoid an upsurge in cases, and any lockdown which may follow. We can only do that with your help and co-operation. I hope we can then all continue to enjoy all that Medway has to offer this summer in the safest possible way."
The latest figures show that 185 people have died from Covid in the Towns.