The draw means the Three Lions will avoid a potential early banana skin fixture against hosts Germany, tournament favourites France, as well Portugal and Spain, who now all find themselves on the other side of the draw.
Finishing second would have meant a knockout tie with a swiftly improving German side.
Instead, Gareth Southgate's side will face the third-placed team from Group D or E—potentially the Netherlands—in Gelsenkirchen on Sunday.
The Dutch finished third in Group D.
Group E is still on a knife edge with Romania, Belgium, Slovakia and Ukraine all on three points each.
Denmark will progress in second, while Slovenia are also through in third.
"I thought we were much improved with the ball," Southgate told ITV after the 0-0 draw with Slovenia.
"We have created some good openings and at the moment it is hard work for us. We are not quite getting that break in front of goal. I think the players who came on did well. I understand the reactions but it is a tough environment
"We tried to win the game by the changes we made. We put attacking players on the pitch."
"That was the aim: to top the group," England captain Harry Kane told ITV.
"We were better on ball, but could not find that final pass.
"We won the group, and now we look forward. The final pass was missing, but we created some chances and had that chance at the end.
"The boys that came on gave us a different dimension, but these games are tough; we've been here before, and hopefully, we can step it up in the knockouts."
England defender John Stones told ITV: "The objective was to top the group and we have done that - it is not always going to be an easy road. It is not going to be easy when we have a target on our back to beat us.
"I thought there was a lot of improvement from the other two games, we found people in the pockets and created more chances - another step in the right direction.
"I can get the fans frustration not taking chances, but that is football - it is never an easy game.
"I am a big believer in beating whoever is in front of us. We need to step-up when it counts and we will work hard on that in training."
