Prior took the decision to step down from the team for the rest of the series mainly because of his woeful form and injuries, saying he was not doing justice to his job.
Cook's batting failure -- he has scored only 115 runs in his last seven innings -- coupled with poor captaincy has prompted several former cricketers to call for his ouster.
Former England captain Michael Vaughan said Cook had the potential to score 13000 Test runs but if he continues to struggle like this, it may spell doom for his career.
"I know the England and Wales Cricket Board has invested a lot of time and effort in Cooks captaincy but sometimes you have to accept that something is not working. Stubbornness is a useful character trait when you are an opening batsman. But when it comes to decision-making, it can be damaging," Vaughan wrote in his column for Daily Telegraph.
"..somewhere deep down, 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.
Vaughan suggested that Cook should be given a break from the game to rejuvenate himself just like some of the greats did in the past.
"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."
"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 play another six years of Test cricket."
Former England opener Boycott was also firm in his view that it's time for Cook to go but questioned the courage of the selectors to take such a step.
"Now that Alastair Cook has declined to give up the captaincy for the benefit of the team, will the England set-up have the balls to sack him," Boycott wrote in his column for the same paper.
"It is important that the selectors do not become stubborn and stick with Plan A in an effort to avoid embarrassment. We all make mistakes and there is no shame in admitting they got this wrong."
Boycott went to the extent of saying that England's selectors should be sacked if they don't remove Cook.
"It might sound harsh to say it, but neither Alastairs feelings nor anyone elses should come into the equation; this is about what is best for English cricket. We cannot afford to do nothing; it is not acceptable.
"I fear that James Whitaker the chairman of selectors is going to just stick his head in the sand and carry on hoping for Cook to make runs and the cricket to change. It will not happen. Leadership is about making big decisions. And if our selectors cannot or will not make those decisions then Downton, as managing director, should sack them."
Boycott was baffled why England players kept pulling and hooking the short balls and fell into India's trap.
"It is as if England have no direction and theres no common sense in the dressing room. Cook needs to go as captain and maybe stay for one more Test as a batsman only. In the famous Ashes series of 1981, Ian Botham resigned the captaincy after making a pair at Lords, releasing all the mental pressure on himself, and then went out and performed heroics at Headingley. Maybe the same process could work for Cook."
Boycott said Prior deserved to go even as he was not much hopeful from his possible replacement.
"Priors wicketkeeping is not special and you get the impression that he needs to go and rest his injuries. He has been playing only partly fit and he is not moving very well for catches or byes. I realise that Joss Buttler and Jonny Bairstow may be no better with the gloves, but they cannot be any worse and we need to get some fresh blood in, some energy," Boycott said.
Former England all-rounder and Test captain Ian Botham said the burden of captaincy is definitely weighing Cook down.
"In my opinion he needs a break from the job and the game. I feel for the captain, he's been the hero and he scored hundreds for fun in his first few games in charge, but now he is patting back half-volleys and nicking wide balls," Botham wrote in the Mirror.
"I would think you've got to fall on your sword at some stage. He's got to say, 'this is not working, it's running through the team now and Im stepping down."
Cook has refused to step down but Botham said it won't work. "It is all well and good the captain standing there and saying, I'm trying very hard and giving it everything but when the brain is scrambled, its scrambled."
Meanwhile, most of the British papers also felt that it will be in the best interest of Cook if he goes.
"Whether the team can support him while he rediscovers the relentless run-scoring of old is another matter. Maybe it would help if the responsibility of captaincy was lifted from him and Ian Bell given the job until the end of the series, so that Cook could start afresh in the Caribbean in April, in Englands next Test series," wrote Guardian.
The 'Daily Telegraph' also drew a comparison between Indian captain MS Dhoni and Cook, saying the Indian outsmarted the hosts leader. The paper praised Dhoni's many a tactics, specially, peppering England batsmen with short balls.
"Dhoni has made a career out of doing the unexpected. Regular Indian Premier League watchers see it every few days with unusual selections and bowling changes and batting promotions, and most famously in the 2011 World Cup final when, despite being hopelessly out of form, he promoted himself to No 5 and won the match with a superbly calculated 91 not out. He did it without even consulting Gary Kirsten, the India coach."
"But ...the reality is good captains are given not made, and now he has 'England bounced out by India' on his CV. It's like being beaten by Zimbabwe at sailing."
The Independent said it was not sure if Cook will be removed and was critical of team's fast bowler.
"Since England were provided with a pitch to die for, this was a significant reversal. Their bowlers, especially the vaunted duet of Jimmy Anderson and Stuart Broad, who are considered cricketing royalty, were outsmarted by their more canny and sensible India counterparts."