Gareth Southgate’s side opened their quest for global glory free of the pressure which has accompanied past campaigns.
They have, however, raised expectations with the level of their performance, while a favourable draw has seemingly opened up in front of them.
Colombia will provide stiff opposition in the last 16, but Sweden or Switzerland lie in store at the quarter-final stage while the semi-finals will deliver a meeting with either Russia or Croatia.
King believes England should be settling lofty targets, with it possible that a lack of big tournament experience and mental scars could work in the Three Lions’ favour.
The former Tottenham captain told the Daily Express: “We’re almost scared to believe. It’s been so long. Judging by the tournament so far there’s no reason why this group of players can’t go all the way.
“We haven’t seen anything to be scared of so far. The only thing that may harm the team is their lack of tournament experience further down the line when it comes to the knockout games, whether that’s the quarter’s or the semi’s.
“However, the fact they haven’t got bad memories they might go out there and face it head on. It’s exciting.”
England ended up in the bottom half of the draw after resting several key men in a final group stage encounter with Belgium.
A much-changed side suffered a 1-0 defeat, but King believes momentum can be maintained as players brimming with confidence are drafted back in against Colombia.
He added: “Definitely [I’ve been impressed]. This group of players went into the tournament with less expectation on them compared to a lot of England teams over the years.
“They’ve played without fear, expressed themselves, everyone wants the ball. They really believe in what they’re doing and the system.
“All the signs have been good, but there will be tougher tests ahead.
“There’s always pressure playing for your country.”