After an impressive start to Roy Hodgson's reign as manager, the Three Lions now face Italy looking to reach their first semi-final since 1996.
Whilst optimism abounds that England will achieve their objective in Kiev's Olympic Stadium, it would be no surprise either if they returned to their Krakow base preparing to pack their bags for home.
Then thoughts will turn to another meeting with Italy, in Berne on August 15, a friendly that provides the build-up to a tricky World Cup qualifying campaign that begins in Moldova.
It represents Hodgson's first chance to put his own imprint on his squad, having opted thus far to rely on the majority of the men who qualified for the Euro 2012 under Fabio Capello.
And Neville feels his boss will be spoiled for choice.
"This squad is the second or third youngest in the tournament," he said.
"And there are young players to come. (Jack) Wilshere, (Kyle) Walker, (Chris) Smalling, (Daniel) Sturridge, and we would like to see more.
"They will get their opportunity in this next couple of years.
"We know that the manager talks about them and wants to bring them in."
They could not be making the transition at a better time either.
In the eight weeks since he was approached to replace Capello, Hodgson has brought a remarkable serenity to the national side.
It is a far cry from the rancour of South Africa, or indeed many of the squads Neville was a part of, largely because there is no clash of egos.
"This is a squad without ego," said Neville.
"You can talk into a microphone about spirit all you like. They are showing it on the pitch.
"We have big characters in the dressing room but they are all fighting for the same cause."
That includes star man Wayne Rooney and skipper Steven Gerrard, England's stand-out player at the tournament so far.
"He is an outstanding football player," said Neville.
"I have said that for 10 or 12 years and it hasn't changed.
"You can't live with him when he runs forward and he can get to players when he runs back.
"At 32, he is a great age. You are at that point when you haven't quite gone over the hill but feel fully matured and experienced.
"It seems like he is relishing the captaincy. You see him dominating the team and dragging them forward.
"Against Sweden he was incredible. Ukraine was even better in a different way."
Yet Neville is eager to play down the suggestion this new England outfit are a limited bunch, who have opted to follow Chelsea's route to glory.
Whilst he accepts it would be an advantage to be slightly more adventurous, he also believes there are a group of players within the England squad who would fit easily into any other team in the tournament.
"We try to be expansive," he said.
"We don't go onto the training pitch and work on giving the ball away and defending.
"But Spain had 70% possession against Italy and no one seems (bothered about how Italy played).
"Even so, you'd go a long way to find players at this tournament who are better than Rooney, (Joe) Hart, (John) Terry and Ashley Cole. (Joleon) Lescott as well.
"We can always talk about what we haven't got but I'd prefer to talk about what we have."
Little wonder Neville is so enthusiastic about his first coaching role, even if, at times, the adjustment from Sky's high-tech studio is a bit tricky.
"In training I am very relaxed," he said.
"The games are more difficult. I am commentating on most of them.
"You kick every ball. I want these guys to succeed so badly because it is inspiring to see the work they put in.
"They recognise that if they beat Italy they are two games away from a final."
And, as Neville knows, such moments do not come around all that often for England.
He reached the semi-finals of Euro 96 as a 21-year-old - and never played in another.
"If we don't go through I would be absolutely gutted," he said.
"I would see it as a disappointment. There is no point trying to play down the fact that we have got to a quarters and that's par for the course.
"It was an achievement to top our group but it wouldn't be if we were gracefully going home after this weekend."