Bale and his countrymen are gearing up for their Group B opener against Slovakia on Saturday, but the Real Madrid forward is already looking ahead to their much-anticipated meeting with Roy Hodgson's side.
"It is like any derby - you never want to lose to the enemy," said the 26-year-old on Friday.
"I think we've got a lot more passion and pride about us than them. We'll definitely show that on the day.
"I knew [England being in Wales' group] was going to come. It is an amazing game to be involved in.
"For me it is probably the standout game in the tournament in the group stage. It is one we are looking forward to.
"There is no pressure on us. They big themselves up before they've done anything, so we're going to go there and we believe we can beat them.
"They believe they can beat us. I'm sure it will be a very good game; hopefully we can come out on top."
Bale could have played for England by virtue of having an English grandmother, a topic his agent brought up before he made his debut for Wales as a 16-year-old.
It has also been suggested by some that Wales' qualification for Euro 2016 - their first major tournament appearance since 1958 - has vindicated Bale's decision to choose the nation of his birth, but he insisted: "I wouldn't care if I never qualified, I would never play for England.
"[Qualifying for Euro 2016] doesn't vindicate anything. If you're Welsh - look at the rugby, we feel more pride and passion than anyone else.
"It's one of those things. It's difficult to explain but we feel that pride and passion. Look at the national anthem, everyone sings, the whole stadium.
"I remember the Belgium game [in qualification for the Euros], we were all tired [late on] and the whole stadium just started singing it.
"I don't think any other nation would do that. Being Welsh just brings it out of you."