Australia's Prime Minister Kevin Rudd and his New Zealand counterpart John Key have welcomed the arrival of the royal baby.
Mr Rudd said it was a time for "rejoicing", while Mr Key said it was a "momentous day" for the Duke and Duchess of Cambridge.
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Fine start to the week for most but turning wet and windy from Wednesday.
Thousands of people have lined the banks of the Mersey to see Cunard's three flagship ocean liners sail down the river.
Claims that surgeons used an old saw found in a cupboard to amputate a patient's leg are being investigated.