Dallaglio was a key part in the victorious 2003 World Cup-winning side in Australia, where they defeated the home team in the Sydney finale.
England return to the Antipodes for another tilt at World Cup glory next month with victorious captain Martin Johnson looking for similar success as coach eight years on.
Dallaglio has lauded England's turnaround under Johnson, but believes the immensely-capable 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 number one side in the world; they are not the number two.
"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 there 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, where he revisits previous tournaments with the help of fellow rugby glitterati.
The former Wasps flanker describes Johnson in the book as being "bright, cheery and frivolous as eve" as the 2003 World Cup came to a head, while others - including head coach Sir Clive Woodward - 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.
"Listen, he wants to do well," he said.
"He is a winner and wants to be successful so of course he will be under pressure, but in a sick sort of way being under pressure is quite good.
"It is how you respond to that pressure which is important.
"It is the most satisfying job in the world when you win and I would imagine there is no better job you can have than captaining, managing or coaching your own country.
"It is also a really tough job when you lose because you share that with the whole country.
"I think he goes into the tournament [with pressure] but I don't think he has visibly changed. I am fortunate to see a side of Martin Johnson that other people do not necessarily see."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.