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Wales, who are playing in their first major tournament since 1958, will reach the last 16 with victory in Lens.
But they have not beaten England since 1984, and Coleman is staying calm.
"The big thing for us is getting through. It's not about beating England and not getting through," he said.
"I said before we kicked a ball that everyone was looking at this game as a battle of Britain. But it's only another game for us.
"We have to take care of business."
Wales' opening win against Slovakia means Coleman's men top Group B, while England are third following their draw with Russia.
The build-up to Thursday's match - the 102nd between the sides - has been highly charged.
Following England midfielder Jack Wilshere's claim he was part of the superior squad, Arsenal club-mate Aaron Ramsey responded by saying Wales have the best team.
Wales forward Gareth Bale then said he and his team-mates are prouder and more passionate about representing their country than their opponents.
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Coleman does not think those comments will have any bearing on the game.
"We can't worry about upsetting the opposition, whoever they are," he said.
"It was always going to turn into this: 'He said this, he said that.'
"It's about what happens on the pitch. All that other stuff is irrelevant. We don't go into mind games. Let's just get down to business."
Wales have won only 14 of their 101 matches against England, losing 66 and drawing 21.
But this Welsh side ended a 58-year absence from major tournaments and became the first home nation to win their opening game at a European Championship.
Defender Neil Taylor highlights last year's qualifying win over Belgium - then ranked second in the world - as the moment Wales began to truly believe in themselves.
"We got over that massive hurdle," he said. "That was the turning point for this team, when we realised we could be a threat against anybody.
"We know the threat we carry and, on our day, we feel we can beat anybody, whether it's England or anyone else."
Wales manager Chris Coleman has urged his players not to get swept up by the emotion of Thursday's Euro 2016 match against England, saying they see it as "only another game".