The Three Lions bounced back after only drawing with Scotland on Friday night.
Raheem Sterling’s second goal of the tournament was enough for two wins from three games for Gareth Southgate’s side.
And now attention turns to the last 16, with several options available to the Three Lions.
England will now play Germany, who finished second in Group F, with the historic rivals set to face off at Wembley at 5pm on Tuesday 29 June.
Leon Goretzka’s goal ensured Die Mannschaft progressed after Hungary had twice lead at the Allianz Arena.