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Testing has been described as the "biggest constraint" on the education sector as more than 30 Kent schools report Covid incidents, a committee was told.
Kent County Council's (KCC) education director, David Adams, said the "most significant" impact had been at Tunbridge Wells Grammar School for Boys where a whole year group of 224 pupils were sent home to self-isolate.
Just under 200 students were taken out of a Wrotham secondary school in the last two weeks amid coronavirus concerns while Year 11 pupils at Chatham's Holcombe Grammar School were last night told to work at home.
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."
His comments came during a virtual public meeting earlier today where KCC's 10-person cabinet was told about anxieties around schools getting access to Covid tests and that improvements would be needed in the coming weeks.
Around 423 of 600 Kent schools have returned with 160,563 pupils attending since the September restart, representing a 90% turnout, but 34 schools have reported Covid-related incidents which has seen staff or pupils self-isolating.
KCC's leader Cllr Roger Gough (Con) revealed that Kent head teachers had contacted him about the growing issues arising from testing, with some families being told to travel hundreds of miles out of the county to get one.
This comes seven days after the chair of Kent Association of Headteachers, Alan Brookes, said that the whole school return was in danger of "coming apart" unless Boris Johnson's government resolved the imminent crisis.
On testing, Mr Brookes said Whitehall support was "woefully small" after the school he works at in Sittingbourne was sent a total of 10 Covid home test kits to share out among 1,450 pupils and staff at Fulston Manor.
Speaking to his nine colleagues earlier today, Cllr Gough described testing as an "issue" and said: "I think it's important we monitor this closely as a cabinet."
A total of 34 Covid cases have been recorded at schools across 12 districts in the county, excluding Medway, with the majority in east Kent covering 11 schools in Thanet, Canterbury and Swale, including five in Sittingbourne.
Under this, 10 have been reported in north Kent covering Gravesend, Dartford and Sevenoaks; seven in west Kent spanning from Maidstone, Tonbridge, Malling and Tunbridge Wells and six across Dover, Folkestone and Ashford.
This comes alongside a recent national survey conducted by a school leaders' union, NAHT, which revealed that more than four in five schools in England have children not in class because they cannot access a Covid test.
Cllr Trudy Dean (Lib Dem), KCC's main opposition education spokesman, described the track and trace system as "completely inadequate" while KCC opposition leader, Cllr Dara Farrell (Lab), of Ashford, called for swift action.
He said: "The government has made it clear that test and trace needed to be fully operational when the schools went back. That's currently not the case."