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Five other hospital trusts, including two in Essex, have welcomed the news they are to be investigated - after the report into the failings at Stafford hospital.
Colchester Hospital University NHS Foundation Trust, Basildon and Thurrock University Hospitals NHS Foundation Trust, Tameside Hospital NHS Foundation Trust, Blackpool Teaching Hospitals NHS Foundation Trust and East Lancashire Hospitals NHS Trust have been "outliers'' on the Summary Hospital-level Mortality Indicator (SHMI) for the two successive years to 2012.
A spokeswoman for Basildon and Thurrock University Hospitals NHS Foundation Trust said they were committed to improving mortality rates, with all hospital deaths reviewed to identify any lessons that can be learned.
The trust's chief executive Clare Panniker said: "We will fully support the review by Sir Bruce Keogh and believe it can only further support our work in this area.
"A great deal of work has already taken place, and more is under way to achieve consistently high standards of care, including the introduction of a trust-wide quality and safety turnaround programme. This is looking at all areas of patient quality and safety, to ensure everyone who comes here receives high quality care and does not come to any harm.
"Clearly some of these changes, alongside improvements we are making to how we communicate and listen to staff, will take time. However, we are working hard and are committed to making Basildon Hospital worthy of the local community it serves.
"We are working closely with external stakeholders, including regulators, to achieve our aspirations.''
In a joint statement, Colchester Hospital University NHS Foundation Trust chief executive Dr Gordon Coutts and North East Essex Clinical Commissioning Group's clinical chief officer Dr Shane Gordon said: "We take all unexpected deaths very seriously and have been closely monitoring these figures over the past two years, with extensive analysis from the trust, commissioners and the National Emergency Care Team.
"The number of deaths at the trust's hospitals (Colchester General Hospital and Essex County Hospital, Colchester) has been falling progressively year-on-year and are within the expected levels on other indicators.
"Our organisations are working together to understand the root causes that contribute to unexpected deaths. We have implemented a comprehensive set of improvements to patient care, including increased consultant cover in our hospitals, particularly in A&E and admitting wards.''
They said they were "encouraged'' by improvements in the HSMR mortality indicator in the past 12 months but added that they would "continue our relentless focus on improving the quality of care and reducing unexpected deaths''.