The first permanent settler in Avon Park was Oliver Martin Crosby, a Connecticut native who moved to the area in 1884 to study the wildlife of the Everglades. By 1886, enough people had followed that the town of "Lake Forest" was founded. As President of the Florida Development Company, he recruited settlers to the area, many of whom were from England including many from the town of Stratford-upon-Avon in England, who gave the town its name.
Source: History of Avon Park 1
History of Avon Park 2
Government Website - City of Avon Park