The proposed legal move is aimed at uncovering billions of dollars in reparations for victims of the mercenary fighters.
Wagner emerged in 2014 in Ukraine and is suspected by the West of doing the Kremlin's dirty work in countries such as Syria and the Central African Republic -- a charge Russia has always denied.
Read more: Deputy Chief of Staff of Wagner PMC Was Eliminated in Ukraine by Warriors of Khort Special Unit
Jason McCue, senior partner at McCue Jury and Partners, said Wagner and its alleged boss Yevgeny Prigozhin "engaged in a campaign of terrorism" in Ukraine including murder, rape, the targeting of infrastructure and the planting of explosives around nuclear facilities.
"Their purpose was to spread terror and chaos in Ukraine," he told Britain's House of Commons Foreign Affairs Committee on Tuesday.
Ukrainian officials have said Wagner has been sending thousands of soldiers recruited in Russian prisons to the front line, with the promise of a salary and an amnesty.
According to communications intercepted by German intelligence, Wagner group mercenaries may have been involved in atrocities in the Ukrainian town of Bucha soon after the invasion on February 24.
McCue told the lawmakers Wagner had to be stopped and that "every option must be pursued to further protect victims of Wagner elsewhere in the world".
Legal action "on behalf of courageous Ukrainian victims has just this second been commenced" against Wagner group and Prigozhin, he said.
"The claim has been commenced with formal service of a Letter Before Action on Prigozhin and Wagner. This is the first time in the world that Wagner and their likes have been sued by its victims for terrorism, used as a weapon of war, Putin's illegal war," he told members of parliament.
McCue said evidence would be produced before the High Court in London aimed at establishing that "Wagner engaged in terrorism against the Ukrainian people" and that "Putin's war machine engaged in an unlawful conspiracy to deploy terrorism to facilitate their illegal invasion of Ukraine".
The case was being brought by a group of Ukrainian victims in the UK but also "symbolically represents" all Ukrainians who have "suffered loss as a result of the war", he added.
Read more: Wagner Military Group Use a Rare Reincarnation of the Soviet BTR-152 in Ukraine
