Both players have been included in Martin Johnson's 45-man training squad despite serving suspensions for high-profile incidents of violent conduct last season.
Tuilagi received a five-week ban for landing a three-punch combination on Northampton and England wing Chris Ashton in the Aviva Premiership semi-final.
The Leicester centre missed the final and the Churchill Cup, but Johnson and his England staff were already convinced he was a live World Cup contender.
Armitage was banned twice last season, once for clashing with a doping control officer and once for punching the Northampton fly-half Stephen Myler.
Johnson is confident both have the temperament to cope with a World Cup but he has issued a strong warning about the need to behave.
"We can't have guys getting suspended down there for events on or off the field," said Johnson.
"We are in New Zealand. We all know what that is like, it is a goldfish bowl. And you are at the World Cup so you are in a goldfish bowl within a goldfish bowl.
"We need guys who are available to play. We don't need silly suspensions because it puts us all under pressure."
Tuilagi, whose four brothers played for their native Samoa, is in line to make his Test debut in one of England's August World Cup warm-up matches.
The 20-year-old is among a group of five centres in the 45-man squad, alongside Mike Tindall, Matt Banahan, Riki Flutey and Shontayne Hape.
England's 45-man squad included a return for Matt Stevens, six months after his drugs ban expired, and call-ups for the uncapped quartet Charlie Sharples, Mouritz Botha, Thomas Waldrom and Joe Simpson.
The squad joined up in camp on Sunday and Johnson reported that the fall-out from John Steele's departure from the Rugby Football Union had not affected his players or staff.
The RFU's decision to oust Steele nine months into his tenure means they are now in the market for both a chief executive and a performance director.
Steele's failure to appoint a performance director - or even hold any interviews for the post - contributed greatly to his downfall.
Johnson expects to be consulted as the RFU move forward on that appointment and it is understood he believes the performance director has to remain hands-off the senior England team.
"I said to Martyn (Thomas, the RFU chairman) 'you guys have to make the right decision for the future of England rugby'. It is not about personalities. It is about the best structure," Johnson said.
"You're always going to report to someone.
"We know what is going on but everyone is excited to be back in camp and it can seem there is nothing outside these walls at times.
"I don't see it having any effect at all on what we are doing.
"If you ask the players, they want to know about training, about dinner and whether they are going to New Zealand.
"When you have the World Cup ahead of you it has a way of focusing your mind."
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