Speed will take his side to Wembley knowing it is 34 years since they last won at Wembley, with England strong favourites to end the match with one foot in next summer's European Championship finals.
Fabio Capello's men cruised to victory in March's reverse fixture at the Millennium Stadium but Speed warned today that his young Wales side had learnt from that 2-0 defeat.
He also revealed he had a plan to exploit the weaknesses that have seen England fail to win at home in the past year as he looked to mastermind a result that would immortalise him and his players in Welsh sporting folklore.
"We wouldn't be here if we didn't think we would win," Speed said.
"England are a fantastic team. They'll cause us problems, no doubt about that, but we're confident and we believe in the way we play.
"You never know, we might nick a result."
He added: "There's certainly no fear.
"England have got fantastic players and are a great team. Their qualification record is as good anybody's.
"We know it's going to be tough but what a great opportunity, to go there and play against one of the best teams in the world, and really try to put on a good show.
"If you go there thinking negatively, you're just playing into their hands.
"You've got to go there with a positive attitude. You've got to go there believing you can get a result from the game.
"We have looked at England to see where they're strong and see where they're vulnerable."
Speed played down the fact Wales' last Wembley win had come in 1977.
"I don't think we've played that many games there to be honest," said the 41-year-old, who pointed out his side had also made history in Friday night's impressive Group G win over Montenegro.
"I don't think we'd ever beaten a team from the former Yugoslavia up until Friday, so there you go."
He added: "The result against Montenegro gave the players a bit of belief that we're going in the right direction.
"Hopefully we can take confidence from that and have another good performance against England."
Friday's victory, Speed's first in a competitive game since his appointment last year, would pale in comparison to a win against England.
Wales will need to play much better than they did in March, when they failed to recover from conceding two goals in the opening 15 minutes.
"That was our first game, really, and we were still putting things in place," said Speed, who admitted it was "vital" his side started better tomorrow.
"Perhaps we were playing too deep in that game and playing into England's hands a little bit. But I was looking more long term.
"At the same time, I was delighted with the way the players went about it in the second half.
"Because they kept to the game plan, they didn't panic, they didn't hump the ball forward, they still tried to keep playing, and had a bit of success second half.
"That's really helped in our development."
Wales' task has been made all the more difficult by suspensions to former captain Craig Bellamy and midfielder David Vaughan.
"In the past, it's cost us when we've missed big players," said Speed, who confirmed Jack Collison had recovered from a virus but admitted Bellamy was a "massive" loss.
"The aim is to make sure it doesn't hurt as much as it has in the past. It gives somebody else an opportunity to come in. They know what's required of them, they know the job."
Regardless of who steps up, Wales' hopes will doubtless rest with the talismanic Gareth Bale.
Speed said: "You're always excited to watch Gareth Bale play, wherever it is.
"Whenever he's in full flow, it's certainly a sight to behold, because he's a very exciting player and an excellent player, as he showed the other night.
"Hopefully, he can cause England some problems."