As previously reported, groups protesting against the controversial decision to sell the objects at Christie's Hong Kong on November 27 launched an urgent appeal for £20,000 to fund their legal action.
They submitted papers to the High Court on Thursday, October 31, according to the Museums Association (MA), but with an oral hearing apparently requested by the council as early as this week, finding money in time could prove very difficult.
Six Riesco pieces were on show at Christie's London last week. The MA say the auction house have been granted a permanent export licence for the 24 items.
The works, which feature Ming, Qing and Early Period ceramics, were acquired by local businessman and collector Raymond Riesco (1877-1964) before entering the council's collection on his death. There are now 230 pieces in total.
The council aims to use the funds raised to help redevelop the Fairfield Halls entertainment venue. Christie's expect the 24 items to make over HK$113m (£9m).
The judicial review would be based on a challenge that the sale goes against council policy.
MA head of policy and communications Maurice Davies said: "There seems to be a very strong case for requiring Croydon to revisit their decision."