His brother Christopher Perkins became a noted artist, and both boys were educated at Gresham's School, Holt, Norfolk.
Frank attended Rugby School (1902–1904), Gresham's (1904–1907), and Emmanuel College, Cambridge, (1907–1910) gaining a pass degree in mechanical engineering in 1910.
At the beginning of the First World War, Perkins volunteered for the army and, in October 1914, was commissioned in the Royal Engineers.
Convinced that the scheme would be profitable in serving the agricultural tractor market, the two formed their own company, F. Perkins Limited, on 7 June 1932, initially with four employees and based in a rented workshop.
In 1915, while on leave from the Royal Engineers, Perkins married Susan Gwynneth Gee, the daughter of Hugh Roberts Williams.