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At least 51 schools across the county have reported coronavirus incidents - as a Kent school boss says teachers should receive test results within 24 hours.
Around 40% of all cases recorded since the start of the full school return in September have taken place in Thanet, Canterbury and Swale.
Watch: Teachers demand faster Covid results for staff and children
Kent County Council says over the last five weeks it has been told about 16 cases in north Kent schools, including Gravesend, Dartford and Sevenoaks. Another 10 have also been reported at sites in Malling, Maidstone, Tonbridge and Tunbridge Wells alongside five schools in Dover, Folkestone and Ashford.
Currently, schools are limited to 10 Covid test kits to share out with hundreds of staff and pupils.
Alan Brookes, who is the chair of the Kent Association of Headteachers, has warned that testing must improve as the growing "big pressure" faced by schools is linked with teachers needing to self-isolate.
Mr Brookes, who this morning called on the government to consider exam arrangements as children's education continues to be disrupted, said the absence of specialist staff due to Covid can affect the groups of between 300 and 400 students that they teach.
Sittingbourne's Fulston Manor school boss said: "I know teachers are one of the priority professions listed for testing, but it's really important they can get access to one and receive results within a day.
"That way they will miss 24 hours of teaching instead of between three and four days, which then becomes a big problem."
He added: "We had one specialist teacher who had to wait for a week for the test result to come back."
Mr Brookes said a knock-on effect was needing to hire supply teachers, who are "hard to find". He adds that schools have received no extra cash from the Government to finance any temporary staff.
Meanwhile, more than 130 pupils at Rose Street Primary School in Sheerness were told to self-isolate after two members of staff tested positive last week.
In addition, the kitchen at Sheppey's George's Primary School had to close earlier today after a caterer tested positive for the virus, with parents having to provide their children with packed lunches hence forth.
Cllr Trudy Dean (Lib Dem), who is KCC's main opposition education spokesman, said the rising Covid numbers were not "unexpected" and said: "The majority of the cases seem to be amongst adults rather than children."
She added: "A better track, test, trace system is necessary and it has always been essential that teachers get regularly tested."
KCC's education director, David Adams, said the "most significant" Covid case numbers had occurred at secondary schools during a council meeting two weeks ago.
His comments came after a whole year group of 224 pupils at Tunbridge Wells Grammar School for Boys where told to self-isolate after a pupil tested positive for Covid in mid-September.
On September 21, Mr Adams said: "We are seeing at secondary level significant numbers of pupils and staff potentially out of school for a couple of weeks.
"We hope that position might change if there is an increase in test capacity."