Victories over Tunisia and Panama have been achieved, and while they were tempered by a 1-0 defeat to Belgium, they have been consoled by the fact that they have ended in the half of the draw largely considered the easier.
Kane, the captain, believes that the forthcoming last-16 tie against the South Americans represents a significant test.
“This is the moment of truth,” he said.
“Now it is the business end. This is what you put in all those hours for, this is why you work, technically and tactically, for big games.
“Colombia are a tough team and have got some great players and we have to be ready for that.
“There's going to be a bit more pressure on us now but I think it's important for us to have that mentality just to be calm in those situations, enjoy it still. This is what we train for and work hard for, these big moments, and hopefully we can do well on Tuesday.”
The Tottenham striker has also made a strong personal contribution to the England cause, netting five times thus far, including a hat-trick against Panama.
He has admitted that he feels capable of scoring every time he goes out onto the field at present.
“That's especially the case when balls are just dropping in for you and things are going for you,” he said.
“You feel you are going to get chances and that feeling helps you find chances.
“I'm ready for everything, whether it is a penalty, a set-piece or anything. I try to practise different situations and make sure I am ready for anything that comes.
“You just want to be on the pitch because you know a chance will come.”
England last faced Colombia in a competitive fixture in the 1998 World Cup, when goals from Darren Anderton and David Beckham gave them a 2-0 victory in the group stage.