The Premiership has provided eight of the last 10 winners of the Amlin Challenge Cup - including Dallaglio's own London Wasps side in 2003 - and the English charge for the 2010/11 campaign will be led by three former winners in Gloucester, Sale Sharks and Harlequins and Dallaglio believes England will wrench the trophy from the holders, Cardiff Blues, this season.
"Traditionally, English clubs have done very well in this tournament. When you look at the history of the Amlin Challenge Cup, almost 99 per cent of the teams to have won it are English," he said.
"There have to be reasons for that and it's down to strength in depth and the way English clubs approach the competition.
"You can't discount Bayonne and Montpellier, but with the likes of Harlequins and Sale involved, I'm fully expecting an English club to reach the final, if not two.
"Newcastle are very familiar with this competition and will be happy to start with a home game. They are a force up there in Newcastle and you have a great chance of progressing in Europe if you win your home games."
Harlequins, winners in 2001 and 2004, meet Bayonne on the opening weekend in Pool 1 while Gloucester travel to Agen and Sale Sharks host the Spanish side, Cetransa El Savador.
"Gloucester have made a slow start to the season but they are looking to build some confidence in this competition and are very tough at home," Dallaglio added.
"The biggest thing they have on their side is the wonderful support at Kingsholm. No opponent will enjoy playing in front of the Shed."
Leeds Carnegie head to Romania, where they face Bucharest Oaks, while Exeter Chiefs will make their European debut against French Top 14 high-flyers Montpellier.
"It promises to be the best day in Exeter's club history. Every game they play in Europe will be the most wonderful experience for everyone involved in the club, from the players to the fans," explained Dallaglio.
"It's great for rugby to have club like that involved. They have made a great start in the Premiership but some of their players will never have dreamed of playing European rugby.
"Montpellier are doing well in the Top 14, but they don't have a tradition of travelling well in Europe and I know from personal experience that Sandy Park is not an easy place to play."