Ms Parkin was working at a Euro Sports Camps summer camp, based at a public boarding and day school Bradfield College in Reading, in August 2023, when the incident happened on the school hockey pitch.
The teacher, named supporting staff member of the year at the Bournemouth Daily Echo School Awards in 2022, is suing CMT Learning, which operates Euro Sports Camps.
Ms Parkin works as a pastoral lead at a secondary school in Bournemouth and said she was forced to stay off work until November 2023 due to the injuries.
Many schools have banned children from playing British Bulldog and other touch games like tag because of injury risks.
A teacher is suing a summer camp firm after being knocked over when up to 100 children playing British Bulldog charged at her.