While Ireland have not secured a Grand Slam since 1948, England found themselves within touching distance during three of the past four seasons.
But European rugby's ultimate prize eluded them each time - at Wembley, Murrayfield and Lansdowne Road - and it is now eight years since England, under Will Carling's captaincy, last achieved the feat.
Woodward believes nonetheless that his current crop of players richly deserve the mantle of being crowned Grand Slam champions.
"Sunday gives us a huge opportunity, and this set of players deserve it," said head coach Woodward, looking ahead to the Grand Slam mission.
"They are a fantastic credit to the English game - they've taken the England side to a whole new level - and the one little thing left outstanding at the moment is this Grand Slam tag. They want to win it desperately, and I want them to win it desperately as well.
"But they know that it doesn't come easy, as we have found over the years," he added.
"I feel that Sunday's game is the hardest of all the chances we've had - because we are playing against another team who have won four out of four, are playing at home and also have world-class players."