The Swansea City ace insists his side will treat Thursday's game as any other, despite the bragging rights at stake.
The Swansea City centre-back took a kick to the leg during his side's dramatic 2-1 victory over Slovakia on Saturday - their first in a major tournament since 1958.
Despite finishing that game, Williams still required treatment, sparking concerns that he could be a doubt to face Roy Hodgson's team.
But he has since declared himself fit, adding that preparations have already begun for the game, which could see Wales bring themselves to the brink of a place in the knockout stages with a win.
"We've started working on it already and we've got a few days before the next game so I'll be fine," he told the BBC.
"It was a kick and luckily it was on the pad, but it's come up and swollen a bit through the pad - but it's fine."
Saturday's result leaves Wales top of Group B after a last-minute equaliser saw rivals England held to a 1-1 draw by Russia in Marseille.
Wales v Slovakia - EURO 2016 - Group B
Williams admits the win over Slovakia was a memorable day for Welsh football, but insists they will be treating Thursday's clash like any other game, despite the bragging rights at stake.
"We understand everything that comes with it [England], but it's another three points we'll be trying to get.
"I'm just happy that we've got a good start to the campaign. It's exactly what we needed to settle the nerves and give ourselves a chance of getting out of the group."