Kew director Peter Crane said: "Wild plants are under greater threat of extinction than at any time since the last Ice Age."
The UK's Millennium Seed Bank (MSB) is a visionary attempt to save many of the world's endangered plants.
Millions of seeds are being banked at the specially designed site in West Sussex with the aim of saving the seeds of more than 24,000 species by 2010, one-tenth of the world's flora.
Seeds from almost all the 1,400 or so British species suitable for inclusion have already been collected.
Extinction threatens more than 300 UK wild plants, and a quarter of the world's plants could be condemned to vanish by 2050.
The centre, run by the Royal Botanic Gardens based at Kew in London forms the greatest concentration of biodiversity on Earth.
A Kew spokesman said: "Most seeds do not look very exciting but they are tiny miracles of packaging, containing all the genetic information for the next generation of plants."
Kew director Peter Crane said: "Wild plants are under greater threat of extinction than at any time since the last Ice Age."
The underground project is funded by £30m from the Millennium Commission and £9.2m from the Wellcome Trust.
Prince Charles, a keen supporter of conservation issues, will be shown first hand some of the advanced technology involved in the project.
Seeds arriving at the MSB have to be dried, cleaned and checked by scientists.
They are placed when ready in ordinary glass jars and stored in three underground vaults at temperatures of -20 degrees C.
The centre started operating in August.