Many on board the London Duck Tours boat jumped into the water as flames took hold and thick black smoke billowed from the amphibious vessel.
A woman and a child were taken to hospital with suspected smoke inhalation.Further tourists were treated at the scene of the fire, opposite the Houses of Parliament.A police source said the nature of the injuries "could have been a lot worse".
A Scotland Yard spokesman said: "A number of people were reported to be in the water at the time. Several Metropolitan Police units attended and the police helicopter."A number of people were recovered from the water. All 28 passengers and two crew members have been accounted for."
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A lamp in the tower which houses Big Ben is to be switched off for the first time in more than 70 years.
Sir Bruce entertained audiences for more than seven decades.
Work in the tower will also pause over the bank holiday weekend.