The home was built by the couple for Richard’s parents, Nino and Dada Rogers.
Ben Rogers, the son of Richard and Su – who divorced in the early 1970s – said: “Twenty-two Parkside is much more than a family home.
“It is one of the most important buildings my father and mother created – a place where many of the ideas that would go on to influence my father’s work and some of the world’s most celebrated architecture were first tested and explored.
“As a family, we wanted to ensure that this remarkable house would be protected, cared for and shared with future generations, rather than remaining a private asset.
“The National Trust brings the expertise, public purpose and long-term commitment needed to safeguard its future, while opening up its story to students, researchers and visitors.”