The railway was built in 1867 by publishing magnate Edward Lloyd, to supply his various businesses with paper from the Sittingbourne Mill, and runs for 5.6km. It was upgraded to steam from horse-drawn in 1905.
Closed in 1969, the heritage railway has been running since 1970.
The mill is currently owned by Finnish paper company M-Real, who closed it in January 2007. They were initially supportive of the railway, which is run as a charity, and allowed it to continue running.
According to Paul Best, who acts as spokesperson for the railway, "The railway has been running for more than 100 years, and we have always had a rolling monthly contract, but we have been told be have to be out by the end of January. The last train is due to run on Boxing day," he said.
Best says that the railway will not be the only loss if the line is dismantled. "The Sittingbourne and Kemsley light railway is listed by the ICE as historically valuable.
"The first kilometre is on a concrete viaduct, built in the 1920s, and was one of the first pre-stressed concrete structures in the UK," he said.
The railway is now looking for ways to have this viaduct listed, which would prevent its demolition, and so save the railway.
"Swale Borough Council are backing us, and our local MP, Derek Wyatt has written to M-Real's vice president, who replied that he would not talk to more than one party," said Best.
A pumping station built by Brunel was saved in similar circumstances in March, following intervention by TV presenter Jeremy Clarkson. It was due to be demolished, but received a 2* listing at the 11th hour.