Unfortunately, according to Leslie Field (The Queen's Jewels, page 147), Queen Elizabeth II wears this necklace "only on private occasions". IMO, such a necklace would be very appropriate, though, for a 'semi-formal' occasion - such as a film premiere, or a variety performance, for example.
Field also mentions that this necklace was made around the turn of the century by the Revivalist jewellers Carlo and Arthur Giuliano. Which raises the question whether this necklace was in the Royal collection as soon as the early 20th century (from Queen Alexandra? Queen Mary? and later inherited by Queen Elizabeth II?) or if it is a later purchase by, or gift to, Queen Elizabeth II.
If I well remember, there is a better picture of this necklace in Suzy Menkes' book about the British royal jewels - unfortunately, I do not have this book in my library, so I can not make a scan of it.