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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Northwestern Scotland and Northern Ireland face a rain-hit weekend, while the rest of Britain enjoys some bright but generally dry weather.
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Some of the world's biggest football clubs will ask FIFA to move the 2022 World Cup to spring.