The Care Quality Commission says both Colchester Hospital and Essex County Hospital need to make further improvements to their services.
The Trust, which runs both hospitals, has been in special measures since last October.
The Trust says significant progress has been made but there is more to do.
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Showers this evening, dying out overnight.
The Bishop of Norwich has called for unity and calm in the wake of the referendum vote to leave the European Union.
Showers becoming heavy this afternoon, with thunder possible.