How did the Royal family come own so many Leonardo Di Vinci works of art?

Bought them from Thomas Howard, Earl of Arundel (having previously passed through the collections of Leonardo’s pupil Francesco Melzi and the sculptor Pompeo Leoni) during the reign of Charles II.

Leonardo Di Vinci was, secretly, a member of the royal family. His mission was to live and work in Florence and report back the results of all his devious spying. These messages were cleverly encoded in his paintings. The "Mona Lisa", for instance, contained the hidden text "Florence will increase its interest rates by 0.03% in April 1517. Leo over and out. Say hello to the dogs". Hope this helped.

Because they are very rich.  Likely they were also given some by foreign dignitaries to ingratiate themselves to help gain favor from the British royals in deals with Britain.  Possibly some have been taken during wars as trophies and presented to the Royal family as gifts in the centuries up to the 19th century.  I doubt Queen Elizabeth the 2nd has slipped any under her coat and stolen any of them on visits to art galleries.

Indeed the royal family of which nation?

which royal family ?