She accused the Met Police of "finger pointing" after it responded by saying the officer who arrested her had been drafted into London from Lincolnshire Police.
Ms Chambers said the Met "ultimately took over" from the arresting officer and detained her. She has lodged a formal complaint.
A Met spokesperson said: "The arresting officer was from Lincolnshire Police and the complaint has therefore been passed to the relevant force to investigate.
"The Met will assist by providing any relevant information they require."
Chief Inspector Simon Outen from the professional standards department at Lincolnshire Police, said: "We have now received a complaint and we are reviewing the incident, and we are in contact with the complainant to establish the full details of her allegations."
Policing around the Coronation has come under scrutiny after the Met expressed regret over arrest of the head of anti-monarchy group Republic and five other protesters on the morning of the ceremony, despite them having coordinated a legal protest with the force.
In total, 64 people were arrested in London during the Coronation policing operation.
Police said 52 of these related to concerns people were going to disrupt the event. Four people have so far been charged.