"My father always told us how Diana was born on just such a blisteringly hot day, at Sandringham, in July 1961", said the Earl.
"It's another very happy summer's day, half a century on."
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Lord Spencer, who is also celebrating the first birthday of his youngest daughter Lady Charlotte Diana Spencer on 23 July, spoke of his joy at the birth of his nephew's first child on Tuesday morning.
"We're all so pleased: it's wonderful news."
Diana's younger brother is currently playing host to his seven children and two stepchildren, who are staying with him and his wife at Althorp to mark his daughter’s birthday. The family will have even more to celebrate now that Charles has become a great-uncle.
New mum Kate Middleton gave birth to a 'beautiful' baby boy on Monday afternoon, after being admitted to St Mary's Hospital in Paddington in the early hours of the morning.
"We could not be happier," said the Duke of Cambridge, who was by his wife's side.
The beautiful boy, who is third in line to the throne, was delivered in the private Lindo Wing of the West London hospital under the care of a top medical team that included the Queen's current surgeon-gynaecologist Dr Alan Farthing and his predecessor Dr Marcus Setchell.
"Her Royal Highness The Duchess of Cambridge was safely delivered of a son at 4.24pm," said a statement from Kensington Palace. "The baby weighs 8lb 6oz.
"The Queen, The Duke of Edinburgh, The Prince of Wales, The Duchess of Cornwall, Prince Harry and members of both families have been informed and are delighted with the news. Her Royal Highness and her child are both doing well and will remain in hospital overnight."
The birth of the new Prince will be marked at 2pm on Tuesday with a 61-gun salute from the Tower of London and a 41-gun salute from Green Park. The bells of Westminster Abbey will also ring out for three hours to celebrate the baby's arrival.