Traders at Hampstead Antique & Craft Emporium were told at the end of October that the centre will shut on January 7 and they have until January 6 to clear their stock.
Around 25 traders are affected by the closure.
Dealer Alexandra Porter began a petition to fight the market closing and it already has more than 600 signatures.
Camden councillor Linda Chung is exploring the possibility of registering the building as an Asset of Community Value (ACV) which could give the dealers more time to find a sympathetic buyer. Porter said local MP Tulip Siddiq is giving the campaign her full support.
If the plan was successful, then the landlord would need to contact the council when they wished to sell the market. Camden would then notify the interested community group who would then have a six month moratorium period giving them a chance to bid for the property.
Porter said: “With the market recognised as an ACV, we could work with the landlord to find an empathetic buyer that would keep the property as an antiques market with our traders.”
She said the public could support the ACV application by signing the online petition Save Hampstead Emporium and by “writing testimonies about the antique market's importance to them' and its special place in the heart of the community”.
She added: “Our message to the landlord is that the antique market is irreplaceable, a very valuable community asset embedded in the heart of Hampstead since the late 60s, and the property should continue its use as a market for the benefit of future generations.”
The emporium, on the corner of Heath Street and Perrins Court, is a former Victorian stables and has been trading as an antiques centre since at least 1967.
However, the owner of the building, landlord Staplepine, said the Emporium will definitely close on January 7 but it made no comment on its plans for the site.
The petition and information can be found at https://you.38degrees.org.uk/p/Savehampsteademporium