Britain has become a cycling nation ahead of Tour start
(From left) Britain's Christopher Froome, Australia's Richie Porte and USA's Danny Pate ride during a training session of the Britain's Sky cycling team in Leeds on July 3, 2014 - by Eric Feferberg
Brailsford, the general manager at Team Sky, who resigned from his role as British performance director earlier this year, said the journey that Britain had embarked on 10 years ago has culminated in a complete change of approach to cycling in the country.
Not only have Britons won the last two Tours but defending champion Chris Froome is favourite to do so again while fellow Brit Mark Cavendish is hotly tipped to win Saturday's opening stage, which finishes in his mother's home town of Harrogate.
"When we started out 10 years ago, we started out with an ambition around the Olympic Games and then we moved on to Team Sky," said Brailsford.
"With Team Sky we had an ambition of trying to build a team to win the Tour de France, try to win the Tour de France with a British rider and try to do it clean.
"We also had another ambition, to try to get a million more people in this country cycling regularly and last week there were 2.1 million people cycling at least once a week in this country.
"I think it cements really where we've got to as a nation, that we've become a cycling nation in many respects."
Froome and Cavendish are among those who have noted a rising enthusiasm for cycling in Britain, especially in the lead up to the Tour.
Kenyan-born Froome, 29, the Team Sky leader, admits he is feeling extra pressure as the reigning champion.
"There definitely is an increase in pressure element coming back as defending champion, given that we're starting on home soil," said Froome.
"We've got huge crowds out here but I think it's all very warm, positive energy for us."
Cavendish, 29, first rode the Tour in 2007 when it started in London and he said this time the British departure feels even bigger and more exciting.
"The type of support, not just in Yorkshire, but from the whole United Kingdom we've had for this 'Grand Depart' is just phenomenal," said the Omega Pharma-Quick Step sprinter.
"People who lived the Tour de France in 2007 when it started in London still talk about it being an exceptional Grand Depart but I'm sure Yorkshire's going to outdo that," he added.
Froome is determined to buck the recent trend and defend his Tour title.
The official records show no-one has defended a Tour crown since Spaniard Miguel Indurain in 1995, but when asked whether that was due to the difficulty in repeating such a success in a new "clean" era, Froome denied that played a role.
"I'd have to disagree with you there, with the fact that if you've won it once then you're spent for years to come," he said.
"I don't agree with that principle, (but) I do believe that you have pressures coming back as a defending champion having won the Tour.
"You definitely have a lot more on your plate after winning the Tour; time between races just slips away from you, you end up doing a lot more in terms of media commitments, sponsor commitments.
"Life definitely changes after winning the Tour and if anything that's probably a bigger factor compared to being wiped out after winning one Tour de France."
The main challenge to Froome's dominance comes from Spaniard Alberto Contador, 31, who has been in fine form this season.
The twice former winner has had his best start to a season since 2010, winning two week-long stage races and finishing second in three others.
He beat Froome at both the Tour of Catalunya and last month's Criterium du Dauphine, although the Briton was leading the latter until a crash on the sixth of eight stages badly affected him.
Although Froome insists other riders such as last year's Giro d'Italia winner Vincenzo Nibali, Fleche Wallonne winner Alejandro Valverde, Dauphine winner Andrew Talansky or 2012 white jersey winner Tejay Van Garderen, cannot be discounted, he admits that Contador is his main challenger.
"I think Alberto has shown he's definitely in a much more competitive position this year than he was last year," said Froome.
"His run-up to the Tour de France has certainly been a lot smoother, he's managed to get a lot more results in early season than he did last year."