The driver, a 42-year-old female ambulance technician, and the patient, an 88-year-old man, were pronounced dead at the scene.
A male crew member and a male relative of the patient remain in hospital both in a serious condition.
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Direct rail services between Southampton and Brighton will be disrupted until the end of this week.
Wednesday morning's weather for the west of the region
Wednesday morning's weather for the east of the region