Graham Smith and five other members of the group were detained before the ceremony on May 6, leaving them unable to join planned protests.
Police said at the time the six were arrested “on suspicion of going equipped for locking on”, referring to items used by demonstrators to attach themselves to one another, an object or the ground.
Officers were given the powers just days before the coronation, following repeated direct action protests by environmental activists and concerns the same could happen during the showpiece royal event.
Smith, who had liaised for several months with London’s Metropolitan Police before the planned protest, wants a judicial review of the decision to hold him.
“We expect a full apology and public acknowledgement that the Met got it wrong,” he said.
“There were no grounds for detaining us, searching us or arresting us. It was an appalling attack on the rights of peaceful protesters.”
Smith is seeking an admission from the Met that the arrests were unlawful, damages and costs.
He and his colleagues were released more than 16 hours after they were arrested and then told that no further action would be taken against them.
The Met confirmed it had received a claim for judicial review.
“It would be inappropriate to comment on ongoing proceedings,” a spokesman said.
The force previously expressed “regret” that the protesters were unable to join others who held aloft “Not My King” placards as part of their campaign for an end to constitutional monarchy.
Human Rights Watch called the arrests “incredibly alarming”, likening it to “something you would expect to see in Moscow, not London”.
Police arrested 64 people on the day, including three members of a local council-run women’s safety group — that the Met sponsored — for carrying rape alarms.
The Daily Mail newspaper had previously claimed that protesters were planning to throw rape alarms to spook military horses taking part in the parade.