The 30-year-old opener has endured a testing 18 months since he guided England to a 3-0 series victory over Australia in his first Ashes series as captain in 2013.
England were humiliated in the ensuing matches Down Under as they suffered an embarrassing whitewash before going on to lose their two-match series at home to Sri Lanka last summer.
Cook was then stripped of his one-day international captaincy only months before this year’s World Cup while his exemplary form with the bat suffered, too.
Indeed his century against the West Indies in May was his first in almost two years.
Cook, who became the leading run-scorer in Test matches for England in the tour of the West Indies, has also resisted numerous calls to resign his captaincy.
Yet buoyed by England’s displays against New Zealand in both formats of the game this summer, he is optimistic England can snatch the famous urn back from their fiercest rivals.
“It was an incredibly tough time,” said Cook.
“Losing that Test series against Sri Lanka and that fourth day at Headingley is as tough as it can get, so from where we have been if we did win the Ashes at The Oval that would be remarkable, and something I would be very proud of – it would be my best achievement.
“We have a good chance of winning. It is going to be a highly competitive series and we will go in as underdogs because they are the best side in the world.
“But in our home conditions and with what has happened over last five or six weeks and the support we are getting, we have a really good chance.”
Cook and his England team-mates depart for Spain today for a pre-Ashes training camp as the England team build a rapport with new coach Trevor Bayliss.
The 52-year-old Australian has taken over from Peter Moores who was sacked as head coach following England’s miserable World Cup.
“We can’t pretend it’s ideal meeting the coach for the first time a week before the Ashes,” said Cook, who dined with Bayliss last night before England’s departure for their four-day camp.
“It’s the first time I’ve had a coach I do not know at all.
“Obviously, with Peter Moores, Andrew Flower and Ashley Giles, I knew them, so I think it’s really exciting to have a guy totally from the outside and with a totally different set of eyes looking at us.
“The relationship with the coach is massive and I’ll spend a lot of time with him, and I think the guys will spend a lot of time with him, too.
“The guys have played a lot of cricket, and done a lot of training. It’s been pretty much non-stop since the start of the West Indies tour.
“Now it is about meeting Trevor and talking about what will happen over the next seven weeks.”
The Ashes begins in Cardiff on July 8, and Cook spoke of the hunger he and his England team-mates have of preventing Australia from winning their first Ashes on English soil since 2001.
“The senior guys who have been round the block can have that temptation to sit back a little, but just chatting to the guys over the last two or three weeks, they are as hungry as ever,” said Cook, who is yet to score an Ashes century at home.
“I saw Jimmy Anderson (on Thursday night), and as soon as we started talking about cricket he told me what he wanted to do to certain players. This is a guy who has taken 400 wickets so that excited me.”
Cook has revealed there has been no batting practice scheduled for England’s four-day training camp in Spain.
While fielding and bowling drills will be organised during the four-day trip, with Cook also keen to formulate plans to regain the urn this summer, England’s batsmen will not be put through their paces. Despite batting collapses in Tests against the West Indies and New Zealand this year, and with the first Ashes match in Cardiff less than two weeks away, Cook believes a rest is in order for the likes of Yorkshire duo Joe Root and Gary Ballance and their England colleague Ian Bell.
The trio have already endured a hectic workload this year, which has encompassed a World Cup, a tour to the Caribbean and a home series against the Kiwis.
Cook, therefore, believes giving them a break will benefit the team in the long run.
He said: “The guys have played a lot of cricket, (so) we don’t need to constantly train, we don’t lose it in two or three days of not picking up a bat.”