The Three Lions have booked their place in the round of 16 after Raheem Sterling’s strike - his second of the tournament.
Gareth Southgate’s will now play Germany, who finished as the runner-up in Group F, at Wembley at 5pm BST on Tuesday 29 June.
Leon Goretzka’s goal ensured Die Mannschaft progressed after Hungary had twice lead at the Allianz Arena.
Without the late goal from the Bayern Munich midfielder, the 2-2 draw between France and Portugal would have meant Gareth Southgate’s side playing Portugal.
Should England emerge victorious from the last 16 tie, then they would face either Ukraine or Sweden in the quarter-finals in Rome.
A potential semi-final date would involve the winner of Netherlands/Czech Republic vs Wales/Denmark.