Terry Venables' team beat the Netherlands 4-1 at Wembley to finish top of their group and earn a quarter-final against Spain at the same venue on Saturday.
Scotland failed to join England by the narrowest of margins. They beat Switzerland 1-0 at Villa Park and would have qualified at the expense of the Netherlands had the Dutch not scored late in the game at Wembley.
The Dutch went through by virtue of having scored more goals and now meet France in the quarter-finals.
Alan Shearer (right) and Teddy Sheringham (left) scored two goals apiece in a memorable performance by England. Shearer is now the leading scorer in Euro 96 with four goals, striking in all three of England's group games.
Venables admitted to being surprised by the margin of England's victory. He said: "I thought we had a very tough game on our hands and had to get a lot of movement if we were going to get anything from it - and I must say we did that very well.
"The players were up in confidence from the last game and took it from there. They have done really well." England, however, will be without Paul Ince for the quarter- finals after the Internazionale player picked up his second yellow card of the tournament.
In yesterday's other matches, France and Spain qualified for the last eight by beating Bulgaria and Romania.