Speaking exclusively to zurichpremiership.com, Woodward said of the potential double: "That would be great. It's very important, particularly for the team I'm in charge of, to win.
"We want to go to the World Cup with a win behind us, and actually, looking back, I was pleased with what happened last weekend [against France in Marseille]. We lost by a point but it was nowhere near our recognisable side.
"Tomorrow [Saturday] night's a little bit different. We've got all our main players playing and we're playing at Twickenham, and it's kind of a reversal. They've got a lot of their star names not playing and I'm looking at England to win, but the biggest thing tomorrow night is for the huge crowd, it's a full house, to really get behind this team – the atmosphere in Marseille was brilliant."
Of his England soccer counterpart, Sven Goran Eriksson, Woodward said of their contrasting roles: "He's actually done remarkably well.
"Fortunately I don't have the media coverage that he does, but he's doing fantastically well, the big games England are winning, but to me it's still just looking in and I'm not close enough to see what's going on.
"To me there's exactly the same parallels though. The secret for England at any sport is arriving at the big games and arriving at the big tournaments with your players fresh, with no injuries and well prepared. If you can do that, then you give them every chance of winning. You can't go into any sport, in any major tournament and expect to beat the best teams in the world if they have been better prepared than you.
"I think the secret for the Football Association and Sven is to get on with the Premiership clubs. It's not easy, because I know that if I was a Premiership soccer manager or a director of rugby in the Zurich Premiership, I'd want to look after my own players.
"It's a very fine line and we all have to fight our own corner, but hopefully we see it all for the greater good. You want your national teams, your soccer team, your cricket team, your rugby team to do well, and nothing gives me a bigger buzz than seeing England win at football or cricket. I think it's something the whole country gets behind, we are a sports mad country."
Speaking on his country's recent rugby success while some of the other sporting teams are perhaps struggling to find the same sort of form, Woodward said of his recipe for success: "Obviously we're pleased with what we're doing, plus we're currently top of the Zurich World Rankings.
"I think we'll go to the World Cup regardless of what happens tomorrow night with a great squad of players, with every chance of being successful. I think preparation is everything. I think England have always had great players over the last 30 years but I think this time, myself and key people at Twickenham have been able to work in a genuine partnership with the Zurich Premiership clubs.
"The last 12 months especially, we really have had the right amount of access to the players. We've gone into all these big games well prepared, the players have been outstanding and the support from all the Zurich Premiership clubs, the directors of rugby especially, your Dean Richards, your Rob Andrews, your Nigel Melvilles, your non-English coaches like Wayne Smith and Warren Gatland just to name but a few, has been outstanding. All of them, without fail, are desperate for England to go well at the World Cup.
"If you prepare properly you do tend to get on the right side of the luck. You're not saying afterwards you lost by a point, you're likely to win by a point, and I think that's the key to it. It's not rocket science.
"We've got a great set-up here, some brilliant people – Andy Robinson, Phil Larder and Dave Alred and all on the medical side. We're getting a lot of support, but support isn't everything and its no guarantee of success.
"What we're trying to do is eliminate as much of the "if onlys" and give this group of players every chance of winning, and I think that's what we've done. It's not just myself, it's the whole game that is supporting this team."
But with Saturday more particularly in mind, Woodward said: "I'm just hoping that on a warm Saturday evening at Twickenham it's all going to kick-off and the crowd get behind Martin Johnson because the team deserves it.
"We may be in nice surroundings here, but it's not quite so nice at 06.30 in the morning in the gym, I promise you. These guys are working tremendously hard to do something very special in a complete once in a lifetime opportunity. We've given them every chance and I hope it goes well tomorrow night and the crowd get behind them."