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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It has been a chilly night in the Anglia region with temperatures plunging below -6°C at Writtle in Essex.
Cold, bright and frosty across most areas to start but cloudier towards the northwest of the Anglia region.
The Care Quality Commission has changed the rating of Addenbrooke's hospital from 'inadequate' to 'good' following a re-inspection.