St. James Park was named after a hospital that was already there, when King Henry VIII acquired the land. He built the "St. James's Palace" and used the land as a kind of zoo. In 1827 the park was redesigned according to the plans of John Nash.
Greenwich Park was once a royal hunting ground, which was opened in the 18th century for the public. You will have a very nice panorama from the famous "Greenwich Observatory" on the Thames and the skyline of the Docklands.