"For all the resolve... to carry on regardless, common sense should prevail in the interests of the man and his team," former captain Mike Atherton wrote in the Times a day after England fell to a humiliating 95-run defeat to India at Lord's.
Cook has gone 27 test innings without a century and presided over England's 5-0 Ashes capitulation in Australia which was followed by a 1-0 home loss to Sri Lanka ahead of the current five-match series against India.
On Monday, India's modest attack ripped through England's paper-thin defences to take a 1-0 lead in the five-match series, prompting calls for Cook's sacking after the Essex cricketer stubbornly refused to step down.
"It gives no pleasure to write it, but the tap on the shoulder for Alastair Cook should come," Atherton added.
"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 again.
"Batting is not coming easily, and he is not a natural leader of men, so both parts of his game require huge reserves of mental energy. It is hard to see that changing any time soon, so the problems will not miraculously disappear."
Cook appears to enjoy the backing of his board and head coach Peter Moores despite a winless streak that stretched to 10 matches following India's second test victory at Lord's.
Many are not sure whether England have an alternative choice as captain, although Atherton is not one of them.
"There is always an alternative - Ian Bell, Joe Root, Stuart Broad, Eoin Morgan are names that would be worthy of close scrutiny - and, more than that, people can surprise you when given extra authority and responsibility," wrote Atherton, who played 115 tests for England from 1989-2001.
"England lose more than they gain by having an out-of-form Cook leading the side."
Writing in the Daily Telegraph, another former skipper, Michael Vaughan, felt Cook badly needed a break.
"I believe Cook wants the selectors to step in and pull him out of the fire, before it gets so hot that we lose him for good. This is a man with the capacity to score 13,000 test runs," wrote Vaughan, who played the last of his 82 tests in 2008.
"For me, Cook would be best off taking a six-month break and chilling out with his family. Shane Warne missed a year of cricket in 2003 thanks to the diet-pill controversy, and some of his best performances came after that suspension. Geoff Boycott skipped a lot of series during his many years with England and look how many runs he finished up with."
Never one to shy away from expressing a frank opinion, Boycott was even harsher in his assessment of the situation.
"Only Alastair Cook, his wife and family want him to remain as captain - nobody else. He's being stubborn and it's going to take six wild stallions to drag him out of that job," the former opener told BBC Test Match Special.