The toddler is among three people still in hospital following the incident at the weekend.
The force received a report of a boat fire in Lechlade, Gloucestershire, around noon on Saturday.
Officers said the vessel was “away from the bank” at the time and all nine people on board “ended up in the water”.
The nine, including five adults and four children aged from 18 months to seven, were taken to hospital.
Three remain there and are in a “stable” condition. Two of them, including the toddler, have “potentially life-changing burns”, the force said.
Witshire Police added it was a “miracle” that no one had died during the “tragic incident”.
Detective Superintendent Joe Garrity said this was due to the “heroic bravery” shown by two holidaymakers from Wales who were in the area.
He said: “With no thought for their own safety, they jumped into the Thames to help save the lives of those involved, some of whom couldn’t swim.”
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A cordon put in place on the river has now been lifted, Wiltshire Police said.
The force is urging members of the public with “relevant information” to contact them.
