Carole and Michael Middleton have been to visit their ''beautiful'' grandson the Prince of Cambridge.

The proud grandparents arrived at the private Lindo Wing of St Mary's Hospital in Paddington, London, at approximately 3:05pm today (23.07.13) to see their daughter Kate Middleton - now known as Duchess Catherine - and her husband Prince William's first child.

Carole and Michael couldn't stop smiling as they entered the hospital and briefly posed for photographs before they went inside.

The couple arrived in a black cab and were picked up by a taxi at 4:10pm staying with their grandson, daughter and son-in-law for just over an hour.

As they left, Carole spoke to reporters outside.

When quizzed on her grandson, she said: ''He's absolutely beautiful, they're both doing really well and we're so thrilled.''

When asked how both parents were doing, she replied: ''Fabulously. It's all coming back to me.''

When pushed for a hint on the baby's name, Carole smiled and said: ''Absolutely not!''

They then got into their waiting vehicle and drove off.

It is still not yet known when the new family will leave the hospital and return home, however, one of Catherine's aides arrived with a car seat for the tot earlier this afternoon ahead of their departure.

Meanwhile, the birth of the baby prince - who is third-in-line to the British throne after his father and paternal grandfather Prince Charles - was marked with a 21 gun salute.

The traditional ceremonial practice took place with 62 shots fired from the Tower of London, and 41 shots fired from Green Park by soldiers in traditional uniform.