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Up to 3,000 bodies could be stored in three temporary mortuaries which Kent County Council will spend £11 million building.
The morgues will be built at locations in Kent over the next 10 months as part of worst-case scenario plans.
The current mortuary capacity has been deemed "insufficient" to deal with the forecast number of Covid-19 deaths across the county, including Medway.
Cllr Roger Gough (Con), the leader of KCC, said: "Our priority is to ensure that, at all times, there is dignity and respect for those who have lost their lives and consideration for the bereaved."
KCC chiefs say they are preparing for a "worst-case scenario" and also following the advice of Boris Johnson's government.
The mortuaries are expected to operate over varying time periods, lasting from 20 to 40 weeks.
Cllr Gough added: "Kent is not alone in the need to make appropriate preparations for increased mortuary demand and we have a statutory responsibility to take the lead in responding to the coronavirus outbreak in Kent.
"We also have to plan, like every other authority across the country, for the worst-case scenario and to ensure that sufficient mortuary capacity is available should it be required."
"It is crucial KCC takes these steps now so that we are prepared for all eventualities.”
A total of £11m will be invested in the installation of three temporary morgues in Kent, which will be paid from Maidstone County Hall's reserves.
This was approved by KCC's leader as part of an urgent decision on Monday.
The cash will be spent on security, body storage management, transportation services and site clearance, including decontamination and staffing.
"It is crucial KCC takes these steps now"
On Monday, work started on the creation of a temporary morgue in Beddow Way, Aylesford, which is due to be completed by April 20.
A marquee with a floor space of 1,000 square metres is due to be installed in one part of the site.
If called upon, the morgue will likely operate 24 hours a day, with seven-day coverage, to allow reactive responses to the ongoing situation.
Two other temporary morgues will be set up across Kent, but the locations of these have yet to be determined.
KCC's main opposition leader, Cllr Rob Bird (Lib Dem), said he "fully supports" the decision, but has called on Medway Council to enter into a "cost sharing arrangement".
Speaking as the Liberal Democrat spokesman on KCC's scrutiny committee, he told KCC in a letter: 'In the current circumstances, I fully support this decision which needs to be taken for KCC to meet its statutory responsibility."
"However, given the proposed provision is for both Kent and Medway, I recommend that officers should enter a cost sharing agreement with Medway Council as a matter of urgency."
Medway council leader Alan Jarrett (Con) says the local authority will not be able to share costs due to the council's "insufficient" cash reserve level, currently used to cover income losses from assets, such as leisure centres.
Cllr Jarrett has suggested calling on the government to provide more funds.
He later added: "I find it interesting that councillors from other authorities want to say how they think funds should be be spent here in Medway."