Gun salutes will be fired across London on Monday to mark the birth of Britain's new princess and tourism chiefs say the baby is expected to boost visitor numbers to the capital.

To mark the royal arrival on Saturday, many of London's hotels and restaurants are celebrating with regal-themed afternoon teas and London landmarks including Tower Bridge and the Trafalgar Square fountains were lit up in pink on Saturday night.

Proud parents Prince William and Kate were expected to spend the next few days at Kensington Palace before travelling to Anmer Hall, their secluded 10-bedroom mansion on the Queen's Sandringham estate in Norfolk.

The monarch attended church there on Sunday, so it is likely she will meet her fifth great-grandchild for the first time at the private country residence.

In the meantime, speculation over what name might be given to the princess has heated up.

Alice and Charlotte are the bookmakers' favourite but some commentators are barracking for the princess to be named after William's mother Diana, who died in a 1997 car crash.

"As the nation waits, why the Princess must be called Diana" read a headline on the front page of The Telegraph.

"William's late mother was there in spirit, outside the hospital on Saturday, her oval sapphire and diamond engagement ring on the hand Kate used to adjust the sleeping baby's shawl," journalist Allison Pearson wrote in the article.

"William gave his fiancee that ring so that his mother, as he said, could be part of their wedding, and I'm sure her name will be passed on to his daughter in the same spirit of commemoration."

The Star put a photo of Diana on its front page, writing "Fans want the new Princess's name to include a tribute to Wills' mother".