China has recovered five of the bronze heads lost in 1860
The rabbit and rat head sculptures auctioned at Christie's last week - despite the objections of China - are part of a set of 12 such statues.
Chinese bidder Cai Mingchao, who won the auction, is now withholding payment out of protest at the auction.
China says the animal heads are part of a collection of 12 looted from the imperial Summer Palace in Beijing in 1860 when it was sacked and burnt by French and British armies.
The statues once adorned a zodiac fountain, or clepsydra, a type of clock that uses water to tell time.
Every two hours water poured from a different bronze head, as time was traditionally measured in 12 two-hour periods, according to Rosemary Scott, international academic director of Asian art at Christie's.
The statues, commissioned by the Qianlong Emperor, are believed to have been designed by Jesuit Giuseppe Castiglione, along with a number of European-themed palaces and fountains in the 18th Century.
In 1795, according to Ms Scott, an order was given for the copper pipe-work in the fountain to be stripped out and melted down, leaving the clepsydra in disrepair when the Summer Palace was eventually destroyed.
Known as Yuanming Yuan, or the Garden of Perfect Brightness, it was sacked by Anglo-French forces during the Second Opium War in 1860.
The heads disappeared. When and how they were then taken out of China - and in whose hands - remains unclear.
While the locations of several of the bronze heads are unknown, five of the statues are back in China, thanks in part to billionaire Macau gambling magnate Stanley Ho.
Mr Ho bought one, a boar's head, at auction in 2003 and then donated it to China's Poly Art Museum, a state-run organisation that describes its mission as "to develop and display traditional national culture and art, and to rescue and protect Chinese cultural relics lost abroad".
The Poly Museum already had the tiger, monkey and ox heads in its collection, secured in 2000.
According to state-run Chinese news agency Xinhua, Mr Ho also bought the fifth - that of a horse head - for 69.1m Hong Kong dollars (£6.3m) and donated it to China in 2007.
Christie's has declined to comment on reports that the buyer of the rabbit and rat head sculptures intends to withhold payment.
"As a matter of policy, we do not comment on the identity of our consignors or buyers, nor do we comment or speculate on the next steps that we might take in this instance," it said in a statement.