Woodward sees 'something special' in Jones's England
England's 48-14 victory over Samoa at Twickenham on Saturday in their last match of this year meant they have won 22 out of 23 Tests since Jones was appointed after their first-round exit at the 2015 World Cup
Woodward, in charge of England when they beat an Australia side coached by Jones to win the 2003 World Cup Final, believes the current team are developing an all-round games that can pose a threat to reigning champions New Zealand in two years' time.
"If I was an England player I would be going back to my club after the autumn [November] games very excited," Woodward told BBC Radio Five on Sunday.
"They know the big goal is the World Cup in Japan and as a player, deep down, you know you've got a chance and you're going there not to make the numbers."
"What I like about England now is that they can play a whole variety of ways," Woodward added.
"They show some great skills, but when they want to play really tough and go physically at teams they can do that as well.
"To win a World Cup you've got to have a team who can play all different ways and also change tactics during the game."
Saturday's success saw England end their November campaign with a perfect played three, won three, record following wins over Argentina and Australia.
Woodward said Jones deserved the bulk of the credit for England's revival following their World Cup failure. England's only defeat under Jones was a 9-13 loss to Ireland in Dublin in March in the Six Nations.
"It's been staggering to win (22 out of 23) from, for me, what was a shambles in the 2015 World Cup," Woodward said. "To not get out of the pool and lose to Australia and Wales at Twickenham was not a good time.
"Eddie's added new players and it's just the competitive nature of the squad, he's brought a real toughness into the team."
"The senior players also had a great autumn – [Dylan] Hartley was fantastic as captain and [Chris] Robshaw was also really strong – so it's not the young guns coming through."
"Senior guys know they've got a chance in a couple of years' time."
England have not played New Zealand, who wrapped up their 2017 with a 33-18 victory over Wales in Cardiff on Saturday, under Jones. The nations meet at Twickenham next November.
"England would go 50-50 into that game with nothing to fear," Woodward said.
Agence France-Presse