Cook made it abundantly clear, after England's descent to a 95-run defeat against India at Lord's, that he still wants to lead from the front in efforts to battle back this summer.
In three days, England must report to the Ageas Bowl to prepare for the start of the next match in a punishing five-Test series - and will be without Matt Prior after the struggling wicketkeeper announced he was taking a break to deal with injuries.
But for Cook, there will be significant matters arising long before Friday - some within his control, others which are not.
In the latter category is the medium-term future of senior pace bowler James Anderson, dependent on the outcome of an International Cricket Council hearing into his Trent Bridge spat with India all-rounder Ravindra Jadeja.
The preliminary stage of a disciplinary procedure which could result in a four-match ban is scheduled to take place, by teleconference, on Tuesday morning.
Cook will have some input when England's selectors decide, also on Tuesday morning, which playing personnel to retain or otherwise to try to recover from a 1-0 deficit.
Whoever joins him, Cook has satisfied himself that England's Lord's defeat - only their second against India at HQ - was not down to his leadership.
"I think a captain is only as good as the players you have with you," he said.
"I don't think it was because of my captaincy that we lost this game."
He is determined not to leave his post yet, despite the clamour in some quarters for him to do so as his run drought continues and England's sequence of setbacks extends to 10 matches without a Test win and seven defeats in nine.
"I'm desperate to carry on," he added.
"There might be a time when I'm not. But at this precise moment in time, I want to - and I want to be at the front when we win games of cricket."
Cook's 'new era', alongside returning coach Peter Moores after last winter's Ashes whitewash, has stumbled into being - and mediocre returns from senior players, including the likes of Prior and Ian Bell.
Others, including Joe Root and Moeen Ali who shared a century stand before England lost their last six wickets for 50 runs to be bowled out for 223 principally by Ishant Sharma (seven for 74), have fared much better.
"The young guys have turned up and played to their potential," added Cook.
"Myself, Ian Bell, Stuart Broad and Matt haven't played as well as we can.
"The past records are fantastic, to be very proud of.
"But Test cricket is a very tough environment to survive in.
"The game owes you nothing, just because you've done it in the past; you have to keep performing for England - that's what Test cricket is about.
"The selectors have always got to think 'Are we putting the best side out on the park?'"
Mike Atherton, who captained England a record 54 times in Tests up until 2001, wrote in The Times: "It gives no pleasure to write it, but the tap on the shoulder for Alastair Cook should come.
"The cruellest cut would also be the kindest cut, as it would be in this fine cricketer's best interests, so that he can find a way to score runs and enjoy his cricket game."
Michael Vaughan, meanwhile, believes Morgan is the man the England and Wales Cricket Board should turn to now even though the Middlesex batsman is not currently in the Test line-up.
Vaughan, who enjoyed a successful stint in charge of England between 2003 and 2008 when he led the team in 51 Tests, wrote in the Daily Telegraph: "For me, Cook would be best off taking a six-month break and chilling out with his family.
"Resting him now might look like a harsh decision, as if you were shooting down a loyal servant. But, in fact, it would be a kindness to protect Cook from the strain that comes with representing England day in, day out. I want to see him playing another six years of Test cricket.
"In the meantime, I would do something radical. I'm sick of seeing us do things by the book.
"The most important event for England ahead of next year's Ashes is the World Cup. So, how about bringing in Eoin Morgan as captain for the rest of this series?
"The England team is crying out for someone with a different viewpoint and Morgan has a lot of tactical awareness and a strong personality. Clearly it would be a risk. But it might be time to throw the dice in the air."
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