The three men and two women are the lead claimants in the reparations case.
The five association members will be seeking general compensation of $81,900 each, Muthoni Wanyeki, the executive director of the independent Kenya Human Rights Commission, said.
The non-governmental organisation has been documenting the torture claims and helping the veterans to prepare their case.
Thousands of Kenyan peasants were rounded up and forced into camps by the British during what was known as the Mau Mau uprising against colonial rule.
The UK has indicated that the claim is invalid because of the amount of time that has passed since the alleged abuses - and that any liability rested with the Kenyan authorities after independence in 1963.
The core of the uprising was formed by members of the Kikuyu tribe, along with smaller numbers from other tribes.
The veterans want the British government to acknowledge responsibility for atrocities in the pre-independence era and to compensate them.'Barbaric treatment'
The Mau Mau, which started as a grassroots Kikuyu movement to recover arable land appropriated by British settlers, evolved into a fully-fledged rebellion in 1952 that demanded Kenyan independence.
|Historians say the Mau Mau uprising helped Kenya gain independence in 1963 [File: ITN]
On October 20, 1952, the British government declared a state of emergency, and launched a military offensive known as Operation Anvil.
Its hit-and-run tactics against white settlers prompted a heavy-handed response from colonial police and allied home guards who rounded up thousands of Kikuyu men and allegedly brutalised and tortured many.
The British described the Mau Mau as a group of "bloodthirsty terrorists", and news reports in the US and Britain during the 1950s made the name Mau Mau synonymous with African tribal violence against whites.
Veterans of the war claim they and their colleagues were made to suffer barbaric treatment such as summary executions, torture, rape, beatings, forced labour and evictions, as the British suppressed the rebellion.
When the UK lifted the state of emergency in 1961, an official report determined that more than 11,000 Africans, most of them civilians, and 32 whites died during that period.
Historians have said the Mau Mau movement helped Kenya gain independence from Britain on December 12, 1963.
The Kenya Human Rights Commission has said 90,000 Kenyans were executed, tortured or maimed during the crackdown, and 160,000 were detained in appalling conditions.