The shortest distance across the strait is from the South Foreland , some 6 km ( 4 mi ) north-east of Dover in the county of Kent , England , to Cap Gris Nez , a cape near Calais in the dÃ partement of Pas-de-Calais , France . The shortest distance across the strait is from the South Foreland , 6 kilometres ( some 4 miles ) north east of Dover in the county of Kent , England , to Cap Gris Nez , a cape near to Calais in the French ' of Pas-de-Calais , France .