The allegations relate to the Mau Mau rebellion, a Kenyan insurgency which took place in the 1950s against British colonial rule.
Leigh Day & Co solicitors, instructed by the Kenya Human Rights Commission to represent some of those who were allegedly tortured, said the government had applied to strike out the case.
The hearing is due to take place in the High Court in the spring.
Leigh Day lawyers said the government's legal team would argue that the liabilities of the Kenyan colonial administration were passed on to the new Kenyan government at independence in 1963.
The implication is that the current Kenyan government is liable for the alleged torture committed by the colonial regime.
Martyn Day, senior partner at Leigh Day & Co, said: "It is deeply disappointing that the British government is refusing to deal with the substance of this case.
"Our concern is that many of these elderly victims will die while this arcane legal point is being argued in the courts."
A Foreign Office spokesman said: "The UK intends to fully defend these cases."