In the return contest that followed soon afterwards in Australia, England were whitewashed 5-0. Andy Flower stepped down as England coach following the team's return and star batsman Kevin Pietersen was sent into an ongoing international exile.
England then lost a two-Test series at home to Sri Lanka, with opening batsman Cook contemplating resigning as captain after the tourists clinched victory at Headingley.
As if all that were not enough, Cook was stripped of England's one-day captaincy in December, just months before this year's World Cup where the team suffered an embarrassing first-round exit in his absence.
Meanwhile the normally reliable Cook, 30, endured a prolonged slump with the bat before scoring his first Test hundred in nearly two years against the West Indies in May.
"It was an incredibly tough time," Cook said at a sponsor's event at Lord's on Friday.
"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 (the venue for the fifth and final Test starting August 20) that would be remarkable, and something I would be very proud of – it would be my best achievement,” Cook said.
"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, he said.
"But in our home conditions and with what has happened over the last five or six weeks, and the support we are getting, we have a really good chance," Cook said, with England having recently drawn a two-Test series with New Zealand before defeating the Black Caps 3-2 in the ensuing one-dayers and a one-off Twenty20.

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