The Beechcraft B200 Super King Air, a medical transport aircraft operated by Dutch company Zeusch Aviation, crashed shortly after take-off just before 4 pm.
It had flown from Athens to Pula earlier on Sunday and was en route to Lelystad in the Netherlands.
Images on social media showed black smoke and flames rising from the crash site.
All flights to and from the airport were cancelled until further notice. London Southend is a relatively small airport, around 72 kilometres east of the capital.