The RFU are currently without a permanent chairman, chief executive or head of human resources and another senior executive, the director of communications Peter Thomas, left the organisation this week after a turbulent last three months.
Dallaglio, the former England captain and 2003 World Cup winner, fears the RFU will waste the priceless opportunity of hosting the 2015 tournament unless the political shambles that has engulfed Twickenham can be sorted quickly.
"It has not been the best few months for the Rugby Union and the sooner everything can be sorted out the better it will be," said Dallaglio, who was speaking at the launch of ITV's World Cup coverage.
"It requires some strong leadership. The potential up-side is massive if they get themselves sorted out structurally. We have got an amazing Rugby World Cup coming here in the next four years.
"England is a sleeping giant. We have risen as giants once, in 2003, and there is no reason why we can't get back to where we need to be but it can't just be done on the pitch.
"It needs a bit of help off the pitch as well. If that is sorted out we will be a threat and the rest of the world will recognise that."
Dallaglio is confident the political upheaval at Twickenham will have no adverse effects on this year's World Cup campaign and may even, in a bizarre way, have actually helped the England players' preparations.
"All you have read about in rugby is the politics and the structure - the coaches and the players have been able to go about their training camp virtually untouched," said Dallaglio.
"In 2003 every day there was lots of press around the team but it is only going to start now. It might be a benefit."
England have been in camp for the best part of six weeks and their preparations have stepped up in intensity in the last fortnight.
On Thursday, manager Martin Johnson put his players through a behind-closed-doors trial match of two 20-minute halves - potentially a last chance for some to impress before the 45-man squad is reduced in size over the weekend ahead of England's first warm-up international, against Wales at Twickenham next Saturday.
Johnson mixed the teams up - there was no distinct A and B team - but there was one notable absentee in Mike Tindall, who is getting married on Saturday.
Manu Tuilagi took advantage of Tindall's absence, scoring a try and showing flashes of the footwork and the power that make him a strong contender for a place in England's final 30-man squad, which Johnson has to name on August 22.
England's World Cup campaign kicks off against Argentina in Dunedin on September 10.
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