The plans for Anmer Hall on the Sandringham estate were approved by West Norfolk Borough Council in March.
BBC: William and Kate: 'Royal house' plan viewers face vetting
The Queen's Bentley failed to start following a Sandringham church service - until a bishop blessed the motor.
Anmer Hall has been part of the Royal Estate since 1898 and is a short drive from Sandringham House.
BBC: William and Kate: Norfolk Royal mansion changes approved
The house has been part of the Royal Estate since 1898 and is a short drive from Sandringham House.
BBC: William and Kate: 'Royal house' plan viewers face vetting
He teaches science - a subject in which there is a shortage of teachers - at Sandringham School in St Albans, Hertfordshire.
Anmer Hall, on the Queen's estate at Sandringham, will get a new garden room and accommodation converted from wood stores on the site.
BBC: William and Kate: Norfolk Royal mansion changes approved
She died in a crash on the A149 at Sandringham about 06:40 GMT on Monday while on her way to work in Hunstanton.
The residents' petition argued the facility - near Sandringham Road and several other cul-de-sacs - would be too close to a "large suburban area".
Senior members of the family, with the Queen herself in the chair, got together twice a year, during the holidays at Balmoral and Sandringham.
The jigsaw is due to go on display at the Sandringham estate in Norfolk in May before it is auctioned to raise money for Help for Heroes.
Members of the public gathered at Sandringham from early on Christmas morning to greet the Royal Family as they left the service at St Mary Magdalene Church.
Born Diana Spencer, at Park House near Sandringham, Norfolk, in July 1961, she became Lady Diana Spencer after her father inherited the title of Earl Spencer in 1975.
Another friend of the princess said her appetite had deteriorated so much that when she ate a jam tart at Sandringham on Sunday, it was cause for celebration.
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