BBC Television Centre should be listed as a grade II building because of its special architectural and cultural significance, English Heritage says.
The conservation body wants the West London site added to the statutory list of significant buildings.
The Blue Peter garden and the main studios are among parts which have contributed to the "iconic presence" of Television Centre, it said.
The Department for Culture, Media and Sport has to consent to the request.
Television Centre was opened on 29 June 1960, as the BBC's first purpose-built centre for television production.
English Heritage's heritage protection director Peter Beacham said: "This building is not just architecturally important.
"As one of the first purpose-built television studios in the world, it represents the moment when Britain led Europe into the television age.
"The BBC itself is an important part of our British identity and Television Centre has acquired an iconic presence."
The Blue Peter garden could be included in the listed areas
English Heritage is requesting listed status for Television Centre's scenery workshop, its canteen block adjoining the Blue Peter garden, and the central circular building.
English Heritage says it will ensure that listing Television Centre does not affect the BBC's ability to adapt it to changing technology or new uses.
A BBC spokesman said: "The BBC is happy to discuss with English Heritage any proposal it has and we will comment to the secretary of state on the historic and architectural merit of Television Centre in due course.
"The BBC has announced that it does not intend to occupy the whole of Television Centre after 2012 but any reference to detailed development plans for the building and site is premature.
"We recognise the historical importance of the building and will be looking for a solution that best preserves the interests of the BBC and licence fee payer but there are no firm plans currently on the table."
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