The result, a record win for England in a World Cup finals match, means England qualifies for the knockout stage with a game to spare, along with Belgium which also has six points, Reuters reported.
Tournament debutant Panama is eliminated along with Tunisia.
England was 5-0 up at halftime after taking full advantage of a poor Panamanian defense. A header from a corner by John Stones, a penalty from Kane and a beautiful strike from the edge of the box by Jesse Lingard set England on its way.
A Stones header from a well-worked free-kick routine and a second Kane penalty gave The Three Lions a 5-0 lead going into the break.
The England captain, now the tournament's top scorer with five goals, completed his hat-trick when a shot from Ruben Loftus-Cheek deflected in off the Tottenham forward in the 62nd minute.
Kane became just the third England player to score a hat-trick in a World Cup game following Geoff Hurst in the 1966 final and Gary Lineker against Poland in the 1986 tournament.
Panama pulled a goal back in the 78th minute through Felipe Baloy – the Central American nation's first goal at a World Cup.