The former England captain played a key part in the victorious 2003 World Cup-winning side in Australia, where they defeated the home team in the Sydney final.
England return to the Antipodes for another tilt at World Cup glory with victorious captain Martin Johnson looking for similar success as coach eight years on.
Former team-mate Dallaglio lauded England’s turnaround under Johnson, but believes the squad has a better chance of winning the 2015 edition on home soil.
“Hand on heart, England are not favourites,” he said. “They are not the No 1 side in the world; they are not the No 2.
“What can we realistically expect from England in this World Cup? Well, if they got to the semi-finals and played well then I think the majority of people would be happy.
“I don’t think Martin Johnson would be happy. I don’t think the coaches would be, I don’t think the players would be happy but the majority of people would say that is not a bad reflection of where you are at the moment.
“Will this team be better after the World Cup? The answer is yes, undoubtedly.
“For many of them it will be their first experience of a World Cup and I know from my own experience in ’99, we didn’t win that World Cup because we were not ready to win it at that moment in time.
“It would have been nice to win it, but we weren’t ready to win it and we learned huge lessons from it. By the time we got to 2003, we were absolutely ready to win that World Cup.
“I hope this England team enjoy the World Cup, have a great experience. For some of them it will be their last but for the majority of them it will be their first.
“I think that this England team’s time will come four years later.
“Without a doubt, this team is capable of winning in 2015. That is no consolation if they don’t go and win this one because, of course, you don’t know what is going to happen in the future. But this England team are getting better and better all the time.”
Dallaglio was speaking at the launch of his new book World Cup Rugby Tales.
The former Wasps flanker describes Johnson in the book as being “bright, cheery and frivolous as ever” as the 2003 World Cup came to a head, while others started to feel the pressure.
Dallaglio does not believe Johnson’s personality has changed dramatically since then and thinks he is in the right frame of mind heading into the World Cup.