They say the Blue Peter garden and the main studios are among parts which have contributed to the "iconic presence" of Television Centre.
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."
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."